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

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

2010-10-22

arxiv.org/abs/1010.4728v3

Int. J. Theor. Phys. (2012) 51:1-13

Physics

Mathematical Physics

18 pages, correction in Ref. [5]

Scientific paper

10.1007/s10773-011-0872-1

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.

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