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

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.

LaTex, 30 pages, no figures

References in corpus (2)

• The propensity of molecules to spatially align in intense light fields
• The Translation Groups as Generators of Gauge Transformation in B$\wedge$F Theory

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