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

摘要

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