The Field Nature of Time in General Relativity

TL;DR

This paper explores the reparametrization-invariant dynamics of general relativity, emphasizing the field nature of geometric time and providing a new path integral formulation for causal Green functions.

Contribution

It introduces a novel approach to describe time as a field variable in general relativity and derives a path integral representation of Green functions within this framework.

Findings

Time measured by an observer's watch coincides with a field variable.

The constraint-shell action reveals the field nature of geometric time.

A new path integral representation of causal Green functions is derived.

Abstract

The paper is devoted to the description of the reparametrization - invariant dynamics of general relativity obtained by resolving constraints and constructing equivalent unconstrained systems. The constraint-shell action reveals the "field nature" of the geometric time in general relativity. The time measured by the watch of an observer coincides with one of field variables, but not with the reparametrization-noninvariant coordinate evolution parameter. We give new solution of such problem, as the derivation of the path integral representation of the causal Green functions in the Hamiltonian scheme of general relativity.