Out of equilibrium

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Out of equilibrium
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we you have I think some I don't know home but it's infinitely sad that somewhere in the corner of the all the the deal is not looking at me and not laughing sarcastic questions about my presentation well I have made many personal memories of the demons and but will probably saved them and tell about 10 months on some of on other occasions maybe tomorrow and the North might talk with the 1st 2 you go well done there will be a central along the kind creatures also in what I would do it came about but what most importantly I want to stress of that there's a huge field of Monica boom fueled series which are physically very important and which we understand very poorly we just scratched the surface of the is and as I believe the fundamental for our understanding of the problems of the cosmological constant flow of cosmic acceleration is fundamental for our don't understanding called turbulence it's of fundamental for understanding calls hierarchy problem in the standard Model soldiers alone I will let them
formulaic now what the essence of what kind of problem but in the castle in the eye of the problem of the cosmological constant is that in the universe would have to scale 1 is its size cycle infrared scale there on the is the Planck length of what we expect from us if we use although some naive some of the equilibrium till the end calculate the cosmological constant weight typical would get that is all that it is it has even at a scale of al -minus through all ultraviolet skill test Blanc side will obtain the answer about what it is all the blank size however role in reality cosmic acceleration tells us that is some of the Order of infrared us again and the difference between the 2 is a huge number to the fixed and then to adults know that's the problem basically no VIP there was an analogous problem was made consider as problem in the 19th century but we had to ,comma Godhra number huge number which measures which the speaking relates the scale of molecular physics to the scale of everyday life and there is some of whom some analogy between the ratio scales and have garden number but I will probably not expand on this and another problem with 2 jails his side just to as summarize what the Fed does just that with have they need not off to scales of 2 fusion differences can now the NRA and so it's interesting to see whether we have some other examples and indeed would do with half of that picture of home of after bills ,comma of Cascade which is not the completely correct but it's qualitatively qualitatively with songs In any case I would have of the ratio of infrared and ultraviolet scales which is mostly window of rain off from power of Reynolds found what it could be very large also end of the most interesting but of physics of turbulence develops between the 2 scales in which is called the inertial range in now another example of how to large-scale so is the fact that in the Standard Model a habit that hierarchy problems and I will probably to say something about that later now I shells
keep a few of the simple exercise on a Caribbean Field here I only want to those with high hopes we don't have much time but but but I want to see the tool can be a 1 teacher of gnomically John Green functions in comparison with the standard Green functions to which we get used to but none equilibrium Green functions which arise when you have power the different In and Out state than the system develops it's not not remain the same but I defined like that and it they don't satisfy operator product expansion and all views all the usual properties of Powell we tried to calculate their magic supposedly do will want to calculate their matches for that we have to take some time to sometimes of stop-loss Infinity's sometimes to minus enchanting and then the belief that our few the attends books would value about the asthmatics is the case in the middle of obviously meeting procedure more deals than to someone uninteresting factors it is not just to the asthmatics but which satisfies that's an important part of which satisfies that usually usual rules all of unit tried to visit the region such as the boy now all what happens in the the non-unitary sees in on unity unity is that when we calculate according to the previous rule the summer probability would take the asthmatics but will get the answer over which is greater than what from their he's so that naive unitality is actually broken the reason for that but I shall explain the reason a moment but they just have go back yeah the reason for that disaster speaking I'm going to expand on the is a roughly speaking I have is that while the Green functions as which satisfies equations of motion Amanda all the usual properties is the ratio of these dramatic famine the asthmatics should be actually it because of brief the amplitude with obtained from the Green function is a relative amplitude it is the probability provided that the vacuum doesn't break down at the end of the month Will 1 of
the questions which is which I will leave unanswered unfortunately is so maybe we can interpret it as a as the space-time interpretation of non-unitary few series of whether we can make use of nonunion to cftc which are important and beautiful but that's unclear
what is important to me that that's another teacher of this canonically Puma approach which ended but now there is that the usual cutting rules for which provides all provide us with the unit today I've not satisfied in this namely the non-excludable firemen diagrams are basically the same as the usual find items except that the time is to evaluate them we will be talking about the Qantas double-digit Contras in time and was later but at the moment it's enough just to always say that the so-called swing get Caldas techniques which replaces Fineman diagrams in canonically bloomed case the technique which provides us with even even out of college Green functions is that you draw the same diagrams but you associate platform minus of the beach but now we can try to derive perturbed to Viviyan tied to conditions optical seated in which tells us that the imaginary part of the amplitude is actually a product also left and right at the end of the day it is sold here in the views of the amplitude which complex conjugate to this wine and we have the normal unit but the there could be a some anomalous pieces you know in on a clear view of which I call spiders which which cannot and will which basically means that vacuum the both spiders are very obvious that in the stands in the stable case than the back the stable of those spiders are equal to 0 but a full absence of spiders is requirement for permanent and here I can't resist the temptation to 0 "quotation mark to you some of the character of from the very famous Russian who said that until well people think that eternity is something grandiose but maybe it's just an old dirty hot .period ideas until that so In fact intended to probably requires the absence of spiders contrary to the subpoena but when also mean that well left for now
let me give you 1 more thing separated example students from all over the a which is very well known and but the example of anonymous which displaced is maybe I should have explained that at the beginning but my point is that a very different economic blueprint phenomenon of AID elated by the technique and by their ideology which by using to describe and that's why in order to develop the intuition it's very important to actually collect and analyze as many examples as you can so that's the explanation of the fact that time actually there are considering some well-known thinks about a slightly viewing them at the slightly different than the soul let's consider production of particles of light elected by the constant electric field this problem which was analyzed and thousands of papers but what Inter and let me fester Betty B. Fletcher they briefly describe how it has sold its soul of possible that would have declined Gordon equation has beaten here will take that a potential only 1 exit component of that the top the each year approximately and of Medicaid is larger which would take the mold of and it's easy to see that wkt condition is satisfied and this is approximately the wave function and that there breakdown of wkt Valente is of the sort of and after that have again WTP you but we have not a single exponential but to exponents of 2 ways of running in opposite directions and we calculate the exact number induced coma and not a simple reason dues go into this type bottled it would be a reflection coefficient here which is with which is eaten here so there the case efficient in front of end nonetheless that only difference from the commitment if you calculate the equilibrium current which is in of but in Alton Maddox settlement it will be the same formula but without the step function and it will be however the Union current who is generated only by the produced by their by generated by article and their generated in this region as the result you get out of the current proportional to admit that a potential without as you see it so that if you don't need calculating to begin this month and this is as kind of a new anomaly end so it it is actually quite interesting because people there conference electric shield of what we have done translations synergy obviously in the in and out and the standard inflation synergy will tell us that the current instead would get their current which is leniently rising with time and this is obviously this spontaneous symmetry breaking in the sense that the things become more dependent of their past this there's a higher Hyatt known localities in the universe in in time now there is an interesting feature which I mentioned that be free on the Web board here it :colon I think you know that there are we can do the calculations in 2 ways and I said here the calculation was down and the creation of a new a 0 0 is 0 In the 2nd gage we can take a year to keep going to eat at everyone including your the results but will be different from the difference between 2 results is related to the fact that but if you start to it than that in order to get in order to get a well-defined problem you have to start with vector potentials of which goes to 0 in in time and in space and then you idea by article turned the tough approach to the constant elected he turns out that in the monarch Libyan situation out there another manifestation of these sensitivity is that there are beer and for depends on all all on the order of Salinas in 1 if you 1st take space dimensions to infinity and you get 1 and 4 and 1 gage if you get that if you take time to mention that it the 1st then you get another as another dissolved tho have not done non-commutative limits so gentlemen on the non commute to Flynn it's I think is that was always historically the source of 5 confusions in well starting from clients as well there is that it's not all you see is that we're glad so we got because the correction to 2 the polarization of backing bifurcation proportional to time and therefore would have some infrared divergent so that it is possible to see I will not be at doing this but it is possible to see that if you the calculate some non equilibrium using these diagram technique using this cut off .period modified cut costs Q rules for the for the shrink goes diagrams you will obtain something interesting namely that well defined massive fuel furious the the Green functions not only the expectation of government but all the normal routine functions have unusual infrared evidence of proportional to the timescale proportional to the timescale and after the time hope from the beginning sought to save the time from the beginning end of this explicitly form and that's 1 of the at the summit summation I don't know what will happen after summation of David Justice and that's 1 of the open question and once again you know will never notice of those intraday registers and people never noticed them if if you calculate the even out Maddox element the finance and for free and reduced but physical amplitudes which shot in the magic found they are full of them there full of infrared diverges this Strong back reaction to tool around letter to give slightly ahead of myself the sole
alone but there is 1 more comment on this thing 1 more comment on this think is that time you can calculate you can calculate but this in the high-dimensional space set in lower refused to use the will go on view of the you don't want to he at work because you never told of the students that their leaving an expanding universe when you tell it when you when uncover released surprise store them but it will have to change the worst of that a good area at that but but but but but but but the this expense mean OK but the yet 1 more point about this and I I will move to the next what is that if you perform similar calculations in the static fueled by then you will get this induced density and proportional tool there this formula chair was thought of my is a T-shirt Academy doubt tried similar formalist many times trying to derive it from Thomas Sandman approximations fall it I was always skeptical and I was wrong because well he never would have a father they know considered these exponential factor but otherwise and it seems that although we have a very unusual vacuum polarization normal vacuum polarization is just think duties is just a bit dependent views things depend on on the field strength only while here you may depend on us back to potential which is unusual and I shall just mentioned because I don't have time to go into the following like interesting that they had a similar phenomenon I can't around the center nominal which I do lead to creation of particles on Oct occurred in condensed matter so well that there is of course the kind the naive there will be a part of it is that is that the inner brat breakdown which is just part of production but I mean something more than that that where I think be excite tonic insulators in which instabilities do you basically to the slides back reactions play played a fundamental role and that's I think maybe an interesting analogy for the cosmological constant problem to keep in mind but we don't have time for this and let me go to the other case still remember the name that excite 20 ,comma insulated and let me analysis which through the case which really interests me and this is the dissident de Sitter space the that's of course the idea that this is the spaces highly interesting because of course the acceleration In the end it is defined its musical analytic continuation of from here on it's the all to here are you just take vacancy you make an elite intonation and you know we are considering a monster shields must have quantum field on the CIA and of course when you have a superior Hamas's feels is there there are more surprises there it's of stable perturbations series working well and nothing happens so 1 might think of that but we can do the calculation in the dissenters space which by the way Madam editions of too much Maddox to terminology this is spaces they imagine it's kind of I cannot help and the kindness tickets and in fact imaginative GFT space the end diseases spaces the usual images on anyway but let's look at the magic left right and that Connors here in this form all of now yeah I
which after a changing on becoming more an attitude like that and you have to consider the only thing which makes fiscal sense here is of the region inside the horizon horizon Howard was 1 of my definition the end of Plan R is less than 1 it's a complete lead in and as I said at a time certain temptation to calculate thinks honesty and then analytically continued to at the very end and at the continued to the deceased yeah we can tried the same
strategy with the Blackwall you you see the Black will have very similar in many respects magic no that is similar magic and In the opinion called on you have to consider only at the end of the space there is no such thing as the region inside the horizon the company's spacing is just not great enough to have and this is the genetically you in the car very well and again there's some of instabilities which for the black hole which I will not discuss which are not relevant for me now but basically it's if you take a scalar field into anything if stable and enter the important point is that in this way which is the way some form students who would be in analyzing them and they would need very important there is
no sign of operation that's 1 thing and then will make these with no signficant everything is stable and normal correction stormed through the mass of black hole for all of now it's the the also the synaptic which I wrote before which was nice complete you plead in Natick Chad ethical companies it's not fall anymore when you could continue so you cannot yearly you're dealing with the incomplete landfill space and in this case unit IT will be lost generally speaking because when particle particle can disappear tho something should be done before and although but there you can't prepare some on physical conditions in which the simply genetic would describe physics of I call the black Blackwall on life support but home will at the end and now
I shall explain very briefly what's what do you happened and hello the system should be achieved the soul in this city the European Union but when we integrate all power forward angle it was 1 of the angle the spherical modern we integrate from 1 of vital pie and bowls of crosses and that would put some current we want to calculate some this is precisely the like calculating some of the many bodies system at some of the review in which case you use them Musselburgh tick Inc and so on integrate the problem in from 0 to abate in the usual cases here you the temperature will be to find this units and you integrate integrated like the now with debt with the formerly continuation will want correlation functions at the moment there the deal time and for that you have to deform the conference and the content becomes like that and that this is almost that shrinking Keldysh technique you have the time contol unit agreed to along the time Quantum which is here so this win the account he would correspond to Libya To this continent for this and this quantity of which is physical and this is of what is obtained from my analytic continuation from the From the months 1 that was speaking and it's called being cut got enough contrary to what they actually assumed in the systems they considered it was equivalent to this but it's not equivalent of in general and for a 24 hour please the difference 1 that you can actually do for this country along with number like that and this will be the case you can be preserved thinks as a describing this the other part of the conduct describes the interior of the black hole fall and Businessland describes only the exterior in any case that's a matter of interpretation but what is not a matter of station is that with the current collectors should be issued the calculators this way yeah
no and well-versed in Italy witnesses saying that they also all of them that the problem with this thinkers that it describes all living the region is very limited teaching this breaks his tied 2 2 we can
improve a little bit by considering the expanding universe which responds to although we move the condition that foreign miners and leave the condition for blast it's still incomplete but what we can do is we can try to attach the mean Koski spaces we can try to complete it to make a job as a good company
and the we can do it by considering the following fans let's look at what happens if instead of their look at this in sort of a purely expanding universe let's assume that there was costly space in the infinite passed then there was an expansion and then then we will find something and we will now I'm so this question what some think it will be and so have the sandwich between 2 men cost spaces would have the expanding the seat of the fifth-seeded tastier that's just of course the fine and come complete form unimportant is just an example of what you can and no it's easy to see that with the sand which is a complete space although all it does not satisfy the Einstein equations cost but we aren't we do not care now about sign and we just say that lets see what how how the quantum field will be increased so that assault once again it you can use the justifiably use of their W being and I'm and of the play and it can be used for large enough case then you have a single wave once again I'm they flattered way it appears after Our well API it appears eventually becomes the smaller than no when
KB conference where men can become involved the award of a W K B breaks after that W K B is stores again looks like a stopping point and then you get to Tuaregs financial reflected Dakes financial sector exponentially appears and so on now we can ask the following question but what will happen if you wear actually Gold Creek time to feeding Seoul was started with a safe haven off their Minkoff the space than out there was exponentially expanding universe that we ended up with an income of faith again but the Minkoff face which will be a generally in the excited states the field will not be the same fold they generally you can calculate the Green function ladies and it contains full it contains the 1st time like that and the 2nd time teachers oscillating with data rapidly because the TNT to so with any cost greening the 2nd term with the move and when I left with the question but what is the meaning of the system you can easily calculate the bacon and you'll find the data is given by the boards of forming on me with the temperature will begin with hiking temperature so what will find is that With studded with pure state and we effectively that evolved into the thermal state which is not pure that's in the context of the black hole it's what's called the information paradox of but there is no place to hear the paradoxes is all that is simply indeed black does not correspond to the pure state however the full Green functions is that it does Chris Porter is just in the pure state which is which was which was obtained by the unity evolutionary from most of them from the initial state from the backyard however for any reasonable observer on any observer is a coarse-grained my soul will for humid will look like a thermal state and as it looks like will be looking as if information is lost over
half of course have found all of a sudden not all of the faces the bubbling if all the OK now we have
another feature here what we expect now because the week's effectively created so many particles and they have agreed Asia attractions are we expect some instability which is still remains to be seen but of I want to stress that those a Standard fewer homes that was when you have expanding universe that is everything daily with and nothing remains on all instability remain in fact I think what happens is that since you have permanent creation of particles the density is not disappearing what what it would have not died Lucian but have approach to the practical becomes more and more None relativistic soul it's there but basically we end up with little stated particles as in the limit of lunch time on this but 2 of them and their there this continuous creation which will be that prevent them the question is
will it the question the also question is those particles become highly degenerate and all of them will have 0 my mentor is dependent on contributions momentum danced with you and so it's probably perhaps is the way to understand the entropy and what's that a defeat of space deal just because of the infrared shift In the particles become an honor to be so that's what time is eaten here there the very the standard view it's an interesting new to just think about what would have cases with the infinite blue shift alike would do in a room in the end IDC toothpaste and these blue shift in and I D C 2 space is responsible for but it is responsible for the idiocy of decreased .period gage stink respondents general we are how it is how it is responsible for the gage stink respondents very simply because of the scale factor the mass of the whole chain disproportional the fall Wal-Mart the small for the open string go away and as a result in such spaces With the infinite Lucia the sting fearing the withheld from calls staying of which have a tower of space but will also have to open strings attached to them to do the box and this open strings they basically have our own lives mustered only mustered mulled over much most go away and so this is for the Aunt Ida for the decedent held for infinite trenches and that perhaps perhaps creates horizon entered but that remains to be I don't believe this the more explicitly they will not the I will I will now be mansion while 1 more view of ,comma which shows about which we must expect instability and the the quantum of stability in the dissident case by the way I should have started should have set already and that classical of the stability of their this is a space it was of course started later in all possible details like people and of the conclusion is that for small enough perturbations stable however 1 In 1 the my claim is that it is unstable is just impossible to have to do is to have when you try to that's possible explanation of why we don't see huge huge cosmological constant is simply is unstable and that's the end of a small calculations which shows a new basically the same thing let's consider the vacuum manager of calculate back manager and let's do it in the following way perhaps from classical magical completion that and we want to find an effective and and also what the calculations in the theater shows is that this is the basically the expression for these diagrams and and then for all this is done for the baiji Davis vacuum but for a lot of states universe by status as that most stable until it is released unstable back in favor of this and it turns out that indeed to this there is non-zero imaginary part now yet again let us know Gold tools company is as I said this I think quite important to consider then Google globally complete candor ,comma collagen is a good country faces and those sandwiches they wears genetically complete but it would be more interesting for us to start with the Einstein's theory to have some solution of Einstein's theory and then see what happens to the and the solution is costs very well known that the solution is the global refuses space which you also obtained from this year by some simple analytic continuation and changes amenable and that the men and their expression for the Natick MA and as I said already stable on the final hole was let's see what happens to these deceit affinity In there in quantum Theatre well 1st of all it's very important whether they're in the vicinity this uh this space has of course had huge synergies inherited from a CIA with started from the honest here than we analytically continue and of course all those operations which were present promise here they don't go anywhere they just get analytically continues so we have this sort of huge imaging In particularly if you calculate the expectation value and at that point on the on this here on the side of a lot better to say this about 5 square about the because because of the number of Wilson's all points of the the if you calculate if you calculate to ferry energy momentum Council once again as some trivial answer if this image is present so basically the synergies of makes it impossible to have more interesting physics it's a bad reaction is always so small now however my point will be once again as it was with the electromagnetic production my point would
be that the synergies spontaneously broken and we do have a lodge that reaction in these problems it is there's a convenient way to calculate thanks in the global space let me explain the waters of the Aegean where have the rose diagram for which is just 2 and a low a quarter of all cylinder and so I want to to do that because I think is that we're supposed to want to calculate the one-point functions there are about 100 the Red bonding response to the at the inside of the flat triangle the space inside this triangle is the diseases space is a plonker page turned on the tap on its head and that Plunkett pages fell by the way it would be the same triangle but universe for GAC have it describes contracting unit of the vision of the past and the university and in the future it becomes a point so this is the contract then it can this of course now people never consider this and correctly and because the fusion unstable contracting it's not global global deceit is stable but contracting Franca Abacha original stable glass in class but we see a strange thing which I don't know how to interpret but that the the calculation of fact that people want to know one-point functions In fact the defeat universe watchful .period function life was not like operation we can't help you build calculation in the contracting universe because not and the global and that simplifies things because when you calculate using tree recovers to technique the sticky unlike find months is causing namely the only interim all the advertisements all I'm Shingo gelded diagrams contributing to this . 1 .period functional will lie all you find that passed last light cold but these inside these past like "quotation mark like Poland lies inside the the boundaries of the type on Korea pitch and I concur Indian Ponca I would be would be updated by changing future into passed by and that sort of that gives us some calculation advantages because it's very easy aromatic is of course very simple to deal with them and you can't perform they can't calculation will only show you media or that I will give you just that the speed of the game Uganda formulate some of those the 5 wishing the Keldysh rules by using heroin III called sleeve and arrows of times each party have individual over time and I hope that quotation is not lost here I recognize some hidden "quotation mark but 2 of the anyway if you don't don't worry will not impede your brother is this but as anyway the rule is that this is the Green function and you associated with outgoing our age include incoming fish stock and and you calculate diagrams will probably keep the part of it's just straightforward calculation of fundamentals the important thing is that you get this carrying behavior like that and as a result I will give give you the is that is something that correction to the Green function "quotation mark the correction to the depicting function can be contains 2 terms which are both obligation incurred they contain explicitly so that probably should have said the 1st of these when you calculate both diagrams you see explicitly look sneak in for a divergent and again those unsolved problem or summing up in the leading log approximation of what said which insists that's not not been done but the divergent themselves can be interpreted in a nice way they can be interpreted as the fact that 1st of all of you obtained from non-zero because of them yield to the character of the Green function is such that it can be interpreted as having fun on 0 occupation number and fabrication and as a matter of fact of these so-called all Slovakia had been considered before and my people and without any injustice just as possible solutions possible Green functions not delete this calculation and they have some real properties but here I have been so because of that people as I understand basically no use new here have no choice when you just do the calculation of the those of election and here I think the visibility by taking absolutely incorrect couples Staley's of conformal and the very 1st thing we have to talk space or over like about basically the answer but it shows that the reaction is if you calculate the Magic's elements of the the state management in terms of the back reaction will be large OK on the 1st summer hint that's something strange is going on when you calculate money when you take these 1st corrections and you you do the calculation of singularities on the horizon You octane assessing the lights not on the horizon but the entire
portal points which are related to the rise in any case that summer the topics to be explored they said something going going on there's this singularity is adequate minus 1 which is I gaged here but probably don't have time to discuss the way to obtain the singularity that's just an interesting point we give it when I started to what you what would now which will power struggles and the Standard Model lot on not yet the sole this is the fear of brief picture that there's a a picture of what what of what happens in the leading role approximation as they said I haven't solved the problem but I I know which diagram with the interpretation of the diagrams which are giving police the In these diagrams I N G markable has tho they they have remarkable sees similarities tool of the diagrams in the fury of turbulence in basically if you with the anxiety which goes through walls diagrams and agrees to pay Shenandoah which depends on the quality of the end of summer recreation the size of operations which also depend on the loggers and then you have to write the kind Natick Collection and this kinetic equation the of contains various that basically what is responsible for the instability of the defeat in it can't because it is just with another a picture of a spider that mentioned the creation from the Vatican the end of this is just an example all of their ability to which you are obtained from this kinetic equations unfortunately the it's not salt so I can I don't know the answer for no portals of occupation on alertness since it was just too it all finished with their name not quite finished as we would like to know what it all means for this standard picture of inflation in the standard picture of inflation and we have to consider the a all that well the single model of installation is the model that we have granted you have that Einstein turned and headed caliph used them in softball that 1 assumes that the cosmological constant is the sole 1 assumes that the view of the euro euro and then 1 finds some self-consistent solutions of for classical solutions for the system the question of which probably should be be a parade through the no why is that there is always the lowest in the most stable solution of this equation named them in cost you vacuum with the shield equal to 0 over another that's it's nothing so why would have cool who and why the pond are sealed so that it started in the excited state why should you be started the site flight the philosophical question is not really a move that you can really ignore such such a philosophical questions but in different movie you may after have sold out from problem I think another problem which I will not mention is that those instability we discussed before then we will be present in this model also but in fact what I just wanted to stress is that of the calculations we Dietz showed that actually did if you have the cosmological constant and it should be at the heart of vandalism no choice of the system must have lost it cannot be staying in the deceit this is a space is not sustainable and it will be there in decaying it will be at producing creative abilities and fall salt in Finland Qantas with picture with a 0 cosmological constant among so in this case known that Einstein said that his biggest blunder was the introduction of the cosmological constant and now we see that she was right because it was small logical constant which created the universe the missile and I think I shall stop here too well you go through to from of of the pleasure of the few issues group With provisional president with was always different ways which With professional respect you have to do also was good the United Nations generously so well this year it's the people's interests and Gladys there just like that ,comma they indicate that best settled today probably should be called secular terms actually because they simply means that you have a system of wealth we will pursue that let me know what the simplest case when you produce massive particles when you produce massive particles on this the current listed becomes proportional to it can be interpreted in different ways ,comma for instance you can say about human form is problem produced particle suffered announced they turn the date of attempts to form a pharmacy and in the pharmacy you get on infrared their divergent coming from all over the world particularly if you have a gapless exciting Asians as the itself but also in the basically I would say that
like in all cases ,comma the Vols 2nd terms indication of instability like for example in normal mechanics of with with secular terms arise because they have some resonance 200 resonances can lead either carriers sought to decay of various things for a or that and that's purely kinetic anonymously said there's a mole in the regions of the secular terms in the just-ended the mountain some knowledge the figures in this part of what they are and that he would ask about the investors and unless or decisions you mentioned the singularity is reached on 1 of the closed the residents review however I don't know I'm there could be no singular personal question is there are those who is behind this war while a lightning and move at the for independent from the question is whether you use the case of the final stage of the review because you know that's what is going on the government is doing the things that make you provide for your family is considered 1 of the worst thing in yes there is what is the average of the top question more of civil war of the what is just so far I just don't know what to of the city what strictly speaking ,comma what what I want what I see is that just the singularity III started with the Green function which depends on these variables that can and Prime end of various Green function has figured this so-called budget data going functional singularity along with the coinciding points now turns out to end the season I don't you know don't you understand very well that there is a bit of another singularity that difficult minus 1 is generated ,comma it is actually the single-entity if you use the conqueror cordoned off and then I think it's a good thing you can calculate that it will it is singularity went 2 points possible in that 1 .period crosses the the horizon if you you have to pointless take these years and then you get single contribution and 1 point you have single item and then they coincide attention on 1 when you cross behind the front you know I miss it might have been I'm very vague about it and I feel it notice some interesting relational things which the details that will be handled differently to you pleasurable and I don't I don't have any indication of what it means and whether it means the fire it sounds so superficially like firewalls which people are discussed and discussing an which I think they're discussing the wrong way but anyway but I don't have much to offer instead of the it's of


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