A path-integral approach to the problem of time

TL;DR

This paper develops a path-integral framework for quantum systems with local internal time, enabling smooth transitions through turning points and offering a new general definition, with implications for the problem of time in quantum gravity.

Contribution

It introduces a path-integral approach to the problem of time, providing a regularized transition through turning points and linking to Gribov problems.

Findings

More regular quantum transition amplitudes near turning points.

Successful transition through a turning point in the model system.

New general definition of transitions in the problem of time.

Abstract

Quantum transition amplitudes are formulated for a model system with local internal time, using path integrals. The amplitudes are shown to be more regular near a turning point of internal time than could be expected based on existing canonical treatments. In particular, a successful transition through a turning point is provided in the model system, together with a new definition of such a transition in general terms. Some of the results rely on a fruitful relation between the problem of time and general Gribov problems.