Geometrodynamical description of two-dimensional electrodynamics

TL;DR

This paper establishes a classical and quantum mapping between two-dimensional electrodynamics and gravity using a first order formalism, introducing extra fields via a BRST boundary term to account for degrees of freedom mismatch.

Contribution

It presents a novel geometrodynamical framework linking 2D electrodynamics to gravity, including quantum-level effects and boundary term techniques.

Findings

Successful classical and quantum mapping between electrodynamics and gravity.

Introduction of extra fields through BRST boundary terms preserves physical content.

Identification of a non-trivial Jacobian affecting quantum features.

Abstract

Two-dimensional pure electrodynamics is mapped into two-dimensional gravity in the first order formalism at classical and quantum levels. Due to the fact that the degrees of freedom of these two theories do not match, we are enforced to introduce extra fields from the beginning. These fields are introduced through a BRST exact boundary term, so they are harmless to the physical content of the theory. The map between electromagnetism and gravity fields generate a non-trivial Jacobian, which brings extra features (but also harmless to the physical content of the gravity theory) at quantum level.