Quantum Gravity Without Ghosts

TL;DR

This paper introduces a gauge-invariant method for constructing quantum effective actions using geometric and fibre-bundle structures, enabling gauge-independent dynamical equations applicable to black hole physics.

Contribution

It presents a novel technique leveraging geometry and fibre bundles to build gauge-fixing-independent quantum effective actions using Vilkovisky's connection.

Findings

Developed a gauge-independent formalism for quantum effective actions.

Adapted the closed-time-path formalism for gauge-invariant fields.

Potential applications include black hole formation and decay studies.

Abstract

An outline is given of a recently discovered technique for building a quantum effective action that is completely independent of gauge-fixing choices and ghost determinants. One makes maximum use of the geometry and fibre-bundle structure of the space of field histories and introduces a set of nonlocal composite fields: the geodesic normal fields based on Vilkovisky's connection on the space of histories. The closed-time-path formalism of Schwinger, Bakshi, Mahantappa {\it et al} can be adapted for these fields, and a set of gauge-fixing-independent dynamical equations for their expectation values (starting from given initial conditions) can be computed. An obvious application for such equations is to the study of the formation and radiative decay of black holes, and to other back-reaction problems.