Reduction of order and Fadeev-Jackiw formalism in generalized electrodynamics

TL;DR

This paper explores the reduction of order formalism within the Fadeev-Jackiw symplectic framework for generalized electrodynamics, clarifying degrees of freedom and simplifying the analysis of higher derivative gauge theories at classical and quantum levels.

Contribution

It demonstrates the equivalence of Ostrogradsky and auxiliary field methods and applies the reduced order formalism to Podolsky electrodynamics, clarifying its symplectic structure.

Findings

Equivalent formulations of higher derivative theories are established.

Reduced order formalism separates Maxwell and Proca sectors.

Simplifies calculations of degrees of freedom in gauge theories.

Abstract

The aim of this work is to discuss some aspects of the reduction of order formalism in the context of the Fadeev-Jackiw symplectic formalism, both at the classical and the quantum level. We start by reviewing the symplectic analysis in a regular theory (a higher derivative massless scalar theory), both using the Ostrogradsky prescription and also by reducing the order of the Lagrangian with an auxiliary field, showing the equivalence of these two approaches. The interpretation of the degrees of freedom is discussed in some detail. Finally, we perform the similar analysis in a singular higher derivative gauge theory (the Podolsky electrodynamics), in the reduced order formalism: we claim that this approach have the advantage of clearly separating the symplectic structure of the model into a Maxwell and a Proca (ghost) sector, thus complementing the understanding of the degrees of freedom of the theory and simplifying calculations involving matrices.