Symplectic Analysis of the Two Dimensional Palatini Action

TL;DR

This paper applies the Faddeev-Jackiw symplectic method to the 2D Palatini action, revealing gauge transformations consistent with Dirac formalism and discussing gauge fixing issues.

Contribution

It demonstrates the equivalence of symplectic and Dirac approaches for the 2D Palatini action and analyzes gauge fixing challenges.

Findings

Symplectic analysis reproduces Dirac gauge transformations.

Constraints lead to consistent gauge symmetries.

Discussion on gauge fixing problems in the symplectic framework.

Abstract

The symplectic analysis, initiated by Faddeev and Jackiw, is applied to the first order (Palatini) form of the Einstein-Hilbert action in 1 + 1 dimensions. The constraints that arise are shown to result in the same gauge transformations that follow from the first class constraints occurring when the Dirac constraint formalism is applied to this action. Problems associated with gauge fixing are discussed.