Functional Change of Variables in the Wheeler--De Witt Equation

TL;DR

The paper introduces a novel method for solving the Wheeler--de Witt equation by exploiting classical reparametrization invariance, enabling tailored wave functions for different cosmological scenarios like closed universes or wormholes.

Contribution

It proposes a new approach using variable transformations based on classical invariance to control the wave function's asymptotic behavior in quantum cosmology.

Findings

Method allows fixing wave function behavior for different universe models

Application to Kantowsky--Sachs spacetime demonstrates effectiveness

Provides a flexible framework for quantum cosmological solutions

Abstract

I present a new way to solve the Wheeler--de Witt equation using the invariance of the classical lagrangian under reparametrization. This property allows one to introduce an arbitrary function for each degree of freedom of the wave function $\Psi$: this arbitrariness can be used to fix the asymptotic behaviour of $\Psi$ so as to obtain a wave function representing a closed universe or a wormhole. These considerations are applied in detail to the Kantowsky--Sachs spacetime.