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 factorisation of phase space 1 If p is even with d = 2p, this action reduces to a surface term.

Topologically massive gauge theories and their dual factorized gauge-invariant formulation

“…The appearance of this topological sector which insures that the gauge symmetry content is maintained, has very intriguing consequences when TMGT are defined on topologically non trivial manifolds [2] or are coupled to matter fields, whether of a fermionic or a bosonic character, since non trivial topological effects then arise. The coupling to matter fields is currently under investigation.…”

“…The dual action possesses the same gauge symmetry structure as the original theory and is factorised into a propagating sector of massive physical variables and a decoupled sector with gauge variant variables defining a pure topological field theory (TFT, for a review see [1]). In this context, dual factorisation is then called "Physical-Topological" (PT) factorisation [2].…”

Non-perturbative dynamics, pair condensation, confinement and dynamical masses in massless QED2+1

“…factorisation of the physical degrees of freedom [11,12] and considers the dynamics of fermions "dressed" by their electric field, as first introduced by Dirac [13]. The dressing of physical charges was elaborated further in [14], for instance, and was shown to greatly improve the soft dynamics [15].…”

“…where ĤΦ is given by (23), and where the Hamiltonian ĤI Φχ is obtained thanks to the Hamiltonian density (11), while…”

Canonical Functional Quantization of Pseudo-Photons in Planar Systems

“…We are considering a functional Schrödinger picture and the difference of sign in the functional derivatives is due to the respective difference of signs in the kinetic term for the fields A and C in the Lagrangian (6) [13]. For k = +1 and from the usual definition of the Hamiltonian H AC = +π i …”