Gauge-invariant factorization and canonical quantization of topologically massive gauge theories in any dimension

Abstract

Abelian topologically massive gauge theories (TMGT) provide a topological mechanism to generate mass for a bosonic p-tensor field in any spacetime dimension. These theories include the (2+1)-dimensional Maxwell–Chern–Simons and (3+1)-dimensional Cremmer–Scherk actions as particular cases. Within the Hamiltonian formulation, the embedded topological field theory (TFT) sector related to the topological mass term is not manifest in the original phase space. However, through an appropriate canonical transformation, a gauge-invariant factorization of phase space into two orthogonal sectors is feasible. The first of these sectors includes canonically conjugate gauge-invariant variables with free massive excitations. The second sector, which decouples from the total Hamiltonian, is equivalent to the phase-space description of the associated non-dynamical pure TFT. Within canonical quantization, a likewise factorization of quantum states thus arises for the full spectrum of TMGT in any dimension. This new factorization scheme also enables a definition of the usual projection from TMGT onto topological quantum field theories in a most natural and transparent way. None of these results rely on any gauge-fixing procedure whatsoever.