Gauge-invariant extensions of the Proca model in a noncommutative space–time

Abstract

The gauge invariance analysis of theories described in noncommutative (NC) space-times can lead us to interesting results since noncommutativity is one of the possible paths to investigate quantum effects in classical theories such as general relativity, for example. This theoretical possibility has motivated us to analyze the gauge invariance of the NC version of the Proca model, which is a second-class system, in Dirac's classification, since its classical formulation (commutative space-time) has its gauge invariance broken thanks to the mass term. To obtain such gauge invariant model, we have used the gauge unfixing method to construct a first-class NC version of the Proca model. We have also questioned if the gauge symmetries of NC theories, are affected necessarily or not by the NC parameter. In this way, we have calculated its respective symmetries in a standard way via Poisson brackets.

Relativistic quantum mechanics of a Proca particle in Riemannian spacetimes

“…A comparison of fundamentals of Dirac and Proca QM shows that the problem of quantization with an introduction of interactions can be solved more easy for a Dirac particle than for a Proca (spin-1) one. However, the solution of this problem for the Proca particle is possible [57][58][59][60][61][62][63][65][66][67] while it meets some difficulties. A consideration of the results obtained for the Proca particle in electromagnetic fields [31,33,39] demonstrates an importance of the ST and FW transformations which result in the Schrödinger form of the PCS equations.…”

“…[57,58]). Another possibility of gauge transformations for the Proca field is an application of the method of gauge unfixing [59][60][61][62][63]. These two methods advocate both the gauge transformation (19) and lengthening the derivatives (6) for the Proca particle in electromagnetic fields.…”