A generalized bag-like boundary condition for fields with arbitrary spin
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| Anzahl der Teile | 62 | |
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| Lizenz | CC-Namensnennung 3.0 Unported: Sie dürfen das Werk bzw. den Inhalt zu jedem legalen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen. | |
| Identifikatoren | 10.5446/38794 (DOI) | |
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Transkript: Englisch(automatisch erzeugt)
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This is a video abstract of the article A Generalized Bag-Rite Boundary Condition for Fields with Arbitrary Spin by Adam Stokes and Robert Bennett. Boundary conditions for the electromagnetic field are routinely used in scattering problems. For a perfectly reflecting surface, the boundary conditions are that the tangential component of the electric field and the normal component of the magnetic field should
00:22
vanish. This is a statement about the behavior of spin-1 bosons at an impenetrable barrier. A commonly used model for the same type of boundary, but instead confining spin-half particles, is the bag model of the nucleon. In this model, quarks are viewed as being confined by a surface that causes the normal component of the fermionic current to vanish.
00:41
It is useful later on to re-express this boundary condition in terms of the Dirac field. Since these two boundary conditions are physically similar, it is natural to ask if they can be unified or even extended to higher spins. To do this, we need a right field of arbitrary spin and a unified language. The approach we use here is the two-spinner calculus, introduced by Bartle, Leendert,
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and van der Bearden in 1928. This makes use of the fact that the Minkowski inner product can be represented using Hermitian matrices. This works by introducing spinner indices running from 0 to 1, as well as the usual spacetime indices running from 0 to 3. This elegant formalism allows the equations of motion for fields of arbitrary spin to
01:20
be written in a unified way. For example, the wave equation for the spin-1 field, shown here, can easily be shown to be equivalent to Maxwell's equations. Equations of motion for fields of higher spin can then be written in the same way simply by using higher order spinners. For example, the spin-3 over 2 field and the spin-2 field are shown below. We begin by showing that the boundary condition for the spin-half field has a natural analogue
01:42
in the spin-1 case. It turns out that this analogous spin-1 condition is precisely the boundary condition usually used for perfectly reflecting boundaries in electromagnetism. We can then write down the analogous boundary condition for the spin-3 over 2 field and the spin-2 field, and so on. This inductive process gives us our main result, which is a generalised boundary condition
02:01
for fields with any spin. For a spin-s over 2 field, the boundary condition contains s factors of the normal to the surface and s Pauli matrices. The expression contains the boundary conditions for the MIT bag model, the electromagnetic perfect reflector, new boundary conditions for fields of higher spin such as the spin-2 graviton.