Pull Back Invariant Matter Couplings

TL;DR

This paper introduces a new algorithm for constructing matter field actions that remain well-defined under degenerate metrics and are invariant under certain pullback transformations, extending standard matter-gravity couplings.

Contribution

The paper presents a novel algorithm for matter field actions that are invariant under pullbacks and valid for degenerate metrics, without using contravariant tensors.

Findings

Actions reproduce standard matter and gravity coupling when metric is nondegenerate

Actions are invariant under degree-one pullback maps

Method extends matter coupling to degenerate metrics

Abstract

An algorithm is described for the construction of actions for scalar, spinor, and vector gauge fields that remains well-defined when the metric is degenerate and that involve no contravariant tensor fields. These actions produce the standard matter dynamics and coupling to gravity when tetrad is nondegenerate, but have the property that all fields that appear in them can be pulled back through an arbitrary map of degree one and that this pull back leave the action invariant when the map has degree one.