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arXiv · 1512.09175

Quantum field theory with a preferred direction: The very special relativity framework

Cheng-Yang Lee
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Abstract

The theory of very special relativity (VSR) proposed by Cohen and Glashow contains an intrinsic preferred direction. Starting from the irreducible unitary representation of the inhomogeneous VSR group $ISIM(2)$, we present a rigorous construction of quantum field theory with a preferred direction. We find, although the particles and their quantum fields between the VSR and Lorentz sectors are physically different, they share many similarities. The massive spin-half and spin-one vector fields are local and satisfy the Dirac and Proca equations respectively. This result can be generalised to higher-spin field theories. By studying the Yukawa and standard gauge interactions, we obtain a qualitative understanding on the effects of the preferred direction. Its effect is manifest for polarised processes but are otherwise absent.

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Cheng-Yang Lee. 2016-02-22. Quantum field theory with a preferred direction: The very special relativity framework. https://doi.org/10.1103/physrevd.93.045011

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