Maxwell - Chern - Simons topologically massive gauge fields in the first-order formalism

TL;DR

This paper formulates Maxwell-Chern-Simons gauge fields in 2+1 dimensions within a first-order formalism, deriving energy-momentum tensors, wave equations, and projection operators, revealing broken dilatation symmetry and the field's scale dimensionality.

Contribution

It introduces a first-order formalism for topologically massive gauge fields, deriving explicit wave equations, projection operators, and analyzing symmetry properties, which is novel in this context.

Findings

Energy-momentum tensors with nonzero traces are found.

The gauge field's scale dimensionality is d=1/2.

A 5x5 Schrödinger form of the equation is derived.

Abstract

We find the canonical and Belinfante energy-momentum tensors and their nonzero traces. We note that the dilatation symmetry is broken and the divergence of the dilatation current is proportional to the topological mass of the gauge field. It was demonstrated that the gauge field possesses the `scale dimensionality' d=1/2. Maxwell - Chern - Simons topologically massive gauge field theory in 2+1 dimensions is formulated in the first-order formalism. It is shown that 6x6-matrices of the relativistic wave equation obey the Duffin - Kemmer - Petiau algebra. The Hermitianizing matrix of the relativistic wave equation is given. The projection operators extracting solutions of field equations for states with definite energy-momentum and spin are obtained. The 5x5-matrix Schrodinger form of the equation is derived after the exclusion of non-dynamical components, and the quantum-mechanical Hamiltonian is obtained. Projection operators extracting physical states in the Schrodinger picture are found.