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arXiv · 1601.08223

Consistent quantization of massless fields of any spin and the generalized Maxwell's equations

Alexander Gersten·Amnon Moalem
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Abstract

A simplified formalism of first quantized massless fields of any spin is presented. The angular momentum basis for particles of zero mass and finite spin s of the D^(s-1/2,1/2) representation of the Lorentz group is used to describe the wavefunctions. The advantage of the formalism is that by equating to zero the s-1 components of the wave functions, the 2s-1 subsidiary conditions (needed to eliminate the non-forward and non-backward helicities) are automatically satisfied. Probability currents and Lagrangians are derived allowing a first quantized formalism. A simple procedure is derived for connecting the wave functions with potentials and gauge conditions. The spin 1 case is of particular interest and is described with the D^(1/2,1/2) vector representation of the well known self-dual representation of the Maxwell's equations. This representation allows us to generalize Maxwell's equations by adding the E_0 and B_0 components to the electric and magnetic four-vectors. Restrictions on their existence are discussed.

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Alexander Gersten, Amnon Moalem. 2016-01-17. Consistent quantization of massless fields of any spin and the generalized Maxwell's equations. https://doi.org/10.1088/1742-6596/615/1/012011

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