On relationship of gauge transformation with Wigner's little group
Abstract
Wigner's little group of a massless particle is ISO(2) which contains rotation and two translations. As well-known, eigenvalues of the rotation are helicity. On the other hand, by S. Weinberg et al., it has been shown that two translations generate abelian gauge transformation by acting on polarization vectors. In this paper, we include unphysical modes and show abelian case result can be generalized to the case of non-abelian gauge transformation. By including the unphysical modes, we obtain Nakanishi-Lautrup physical state condition from the requirement of unitarity of the transformation. As a result, non-abelian gauge transformation is realized as the translation of the little group which acts on gauge group. We also obtain similar results for any spacetime dimensions.
Keywords
Cite
@article{arxiv.1212.1446,
title = {On relationship of gauge transformation with Wigner's little group},
author = {Hiroshi Yoda},
journal= {arXiv preprint arXiv:1212.1446},
year = {2012}
}
Comments
14 pages