A Canonical Analysis of the First Order Einstein-Hilbert Action

TL;DR

This paper applies the Dirac constraint formalism to analyze the first order Einstein-Hilbert action in higher dimensions, identifying the constraint structure and degrees of freedom without eliminating fields via equations of motion.

Contribution

It provides a detailed canonical analysis of the first order Einstein-Hilbert action in arbitrary dimensions, including the constraint algebra and degrees of freedom.

Findings

Identifies primary, secondary, and tertiary constraints.

Determines the phase space degrees of freedom as d(d-3).

Provides the Poisson Bracket algebra of constraints.

Abstract

The Dirac constraint formalism is applied to the d(d>2) dimensional Einstein-Hilbert action when written in first order form, using the metric density and affine connection as independent fields. Field equations not involving time derivatives are not used to eliminate fields. Primary, secondary and tertiary constraints arise, leaving d(d-3) degrees of freedom in phase space. The Poisson Bracket algebra of these constraints is given.