Maxwell–Chern–Simons Topologically Massive Gauge Fields in the First-Order Formalism

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 6×6-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 5×5-matrix Schrödinger 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 Schrödinger picture are found.