Gauge fixation and global phase time for minisuperspaces

TL;DR

This paper develops a method to define a global phase time in minisuperspace cosmological models by gauge fixing, analyzing how the geometry of the constraint surface influences the choice of time and its implications for path integral quantization.

Contribution

It introduces a gauge fixing procedure that explicitly constructs a global phase time in minisuperspaces with separable Hamilton-Jacobi equations, linking geometry to quantization.

Findings

Global phase time can be defined via canonical gauge conditions.

The geometry of the constraint surface constrains the choice of time.

Implications for path integral quantization are discussed.

Abstract

Homogeneous and isotropic cosmological models whose Hamilton-Jacobi equation is separable are deparametrized by turning their action functional into that of an ordinary gauge system. Canonical gauge conditions imposed on the gauge system are used to define a global phase time in terms of the canonical coordinates and momenta of the minisuperspaces. The procedure clearly shows how the geometry of the constraint surface restricts the choice of time; the consequences that this has on the path integral quantization are discussed.