The Canonical Structure of the First Order Einstein-Hilbert Action with a Flat Background

TL;DR

This paper investigates the canonical structure of the first order Einstein-Hilbert action with a flat background and compares it to the first order spin-2 action, revealing differences in their constraint algebra in the weak field limit.

Contribution

It demonstrates that the Poisson bracket algebra of first class constraints in the weak field limit of the Einstein-Hilbert action differs from that of the spin-2 action.

Findings

Weak field limit Poisson brackets differ from spin-2 algebra

Canonical structure involves three generations of constraints

Gauge transformation corresponds to diffeomorphism with field-dependent gauge function

Abstract

It has been shown that the canonical structure of the first order Einstein-Hilbert (1EH) action involves three generations of constraints and that these can be used to find the generator of a gauge transformation which leaves the action invariant; this transformation is a diffeomorphism with field-dependent gauge function while on shell. In this paper we examine the relationship between the canonical structure of this action and that of the first order spin-2 (1S2) action, which is the weak field limit of the Einstein-Hilbert action. We find that the weak field limit of the Possion Brackets (PB) algebra of first class constraints associated with the 1EH action is not that of the 1S2 action.