Global phase time and path integral for the Kantowski--Sachs anisotropic univers

TL;DR

This paper reformulates the Kantowski--Sachs cosmological model into an ordinary gauge system, identifies a global phase time, and computes the quantum transition amplitude using path integral methods.

Contribution

It introduces a novel approach to quantize the Kantowski--Sachs model by transforming its action into an ordinary gauge system and applying path integral techniques.

Findings

Successfully identified a global phase time for the model

Derived the quantum transition amplitude via path integral

Provided a new framework for quantum cosmology of anisotropic models

Abstract

The action functional of the anisotropic Kantowski--Sachs cosmological model is turned into that of an ordinary gauge system. Then a global phase time is identified for the model by imposing canonical gauge conditions, and the quantum transition amplitude is obtained by means of the usual path integral procedure of Fadeev and Popov.