The Electromagnetic and Proca Fields Revisited: a Unified Quantization

Abstract

Quantizing the electromagnetic field with a group formalism faces the difficulty of how to turn the traditional gauge transformation of the vector potential, $A_{\mu }(x)\to A_{\mu }(x)+{\partial }_{\mu }\phi (x)$, into a group law. In this paper it is shown that the problem can be solved by looking at gauge transformations in a slightly different manner which, in addition, does not require introducing any BRST-like parameter. This gauge transformation does not appear explicitly in the group law of the symmetry but rather as the trajectories associated with generalized equations of motion generated by vector fields with null Noether invariants. In the new approach the parameters of the local group, $U(1)(\vec{x},t)$, acquire dynamical content outside the photon mass shell, a fact which also allows a unified quantization of both the electromagnetic and Proca fields.

16 pages, latex, no figures

Cited by in corpus (8)

• Relativistic quantum mechanics of a Proca particle in Riemannian spacetimes
• Group Approach to Quantization of Yang-Mills Theories: A Cohomological Origin of Mass
• Space-time Structures from Critical Values in 2D Quantum Gravity
• Gauge Transformation Properties of Vector and Tensor Potentials Revisited: a Group Quantization Approach
• Algebraic characterization of constraints and generation of mass in gauge theories
• Extended diffeomorphism algebras in (quantum) gravitational physics
• Modular Invariance on the Torus and Abelian Chern-Simons Theory
• Relativistic field equations from higher-order polarizations of the Poincaré group