Eisenhart--Duval lift for minisuperspace quantum cosmology

TL;DR

This paper explores the use of the Eisenhart--Duval lift to formulate covariant quantum equations in minisuperspace cosmology, introducing a Dirac-type equation and providing explicit solutions for certain models.

Contribution

It introduces a covariant Dirac-type equation in extended minisuperspace using Eisenhart--Duval lift, advancing quantum cosmology modeling.

Findings

Derived explicit fundamental solutions for specific models.

Established a covariant Dirac-type equation in extended minisuperspace.

Discussed potential future developments in the approach.

Abstract

We study covariant equations in quantum cosmology of an extended minisuperspace obtained by the Eisenhart--Duval lift. We find that a Dirac-type equation is naturally introduced in the extended minisuperspace. Explicit forms of the fundamental solutions are yielded for specific models. The possible further development in this direction is also discussed.