Polarization Vectors, Doublet Structure and Wigner's Little Group in Planar Field Theory

TL;DR

This paper demonstrates the equivalence of a planar field theory model to a doublet of models through polarization vectors, explores U(1) invariance, and examines Wigner's little group as a gauge transformation generator.

Contribution

It establishes the equivalence of Maxwell-Chern-Simons-Proca and doublet models using polarization vectors and analyzes Wigner's little group in three dimensions.

Findings

Polarization vectors reveal model equivalence

U(1) invariance in momentum space

Wigner's little group generates gauge transformations

Abstract

We establish the equivalence of the Maxwell-Chern-Simons-Proca model to a doublet of Maxwell-Chern-Simons models at the level of polarization vectors of the basic fields using both Lagrangian and Hamiltonian formalisms. The analysis reveals a U(1) invariance of the polarization vectors in the momentum space. Its implications are discussed. We also study the role of Wigner's little group as a generator of gauge transformations in three space-time dimensions.