Reduced Order Podolsky Model

TL;DR

This paper explores the quantization of a simplified Podolsky electrodynamics model, revealing an auxiliary massive vector field and establishing classical and quantum equivalence with the original theory.

Contribution

It introduces a lower-order derivatives version of Podolsky's model and performs detailed canonical and path integral quantizations, clarifying its physical and mathematical structure.

Findings

Identification of auxiliary massive vector field

Explicit Dirac brackets involving both fields

Successful path integral quantization using Batalin-Fradkin-Vilkovisky scheme

Abstract

We perform the canonical and path integral quantizations of a lower-order derivatives model describing Podolsky's generalized electrodynamics. The physical content of the model shows an auxiliary massive vector field coupled to the usual electromagnetic field. The equivalence with Podolsky's original model is studied at classical and quantum levels. Concerning the dynamical time evolution we obtain a theory with two first-class and two second-class constraints in phase space. We calculate explicitly the corresponding Dirac brackets involving both vector fields. We use the Senjanovic procedure to implement the second-class constraints and the Batalin-Fradkin-Vilkovisky path integral quantization scheme to deal with the symmetries generated by the first-class constraints. The physical interpretation of the results turns out to be simpler due to the reduced derivatives order permeating the equations of motion, Dirac brackets and effective action.