A polynomial action for gravity with matter, gauge-fixing and ghosts

TL;DR

This paper presents a polynomial variational formulation of General Relativity coupled with various matter fields, including ghosts, valid in any number of spacetime dimensions, emphasizing its polynomial structure and gauge-fixing approach.

Contribution

It introduces a polynomial Lagrangian density for gravity with matter, gauge-fixing, and ghosts, applicable in arbitrary dimensions, unifying the formulation of diverse fields within a single framework.

Findings

Polynomial Lagrangian density for gravity and matter fields.

Inclusion of ghosts with hyperbolic equations of motion.

Applicable to any number of spacetime dimensions.

Abstract

We give a variational formulation of General Relativity, with coupling to a cosmological constant, to scalar fields, to vector fields and to spinor fields (all with possible mass and interaction terms). Among the matter fields, we include ghosts corresponding to diffeomorphism and Yang-Mills gauge symmetries, with kinetic terms given by gauge fixing conditions leading to hyperbolic equations of motion for all fields. The distinguishing characteristic of our Lagrangian density is its polynomiality, in all dynamical fields and Lagrange multipliers, and its validity for any number of spacetime dimensions.