Nicolai Maps for Quantum Cosmology

TL;DR

This paper constructs Nicolai maps for specific supersymmetric quantum cosmology models, revealing their existence only for certain states and suggesting a probabilistic interpretation of the wave function.

Contribution

It explicitly constructs Nicolai maps for $N=2$ supersymmetric minisuperspace models and analyzes their existence and interpretation.

Findings

Nicolai maps exist only for the empty and filled fermion sectors.

The maps have a natural stochastic interpretation.

Results suggest a probabilistic view of the wave function.

Abstract

We construct Nicolai maps for $N=2$ supersymmetric extensions of minisuperspace models. It is shown that Nicolai maps exist for only a very restricted set of states. In the models considered these are the two states corresponding to the empty and the filled fermion sectors. The form of the Nicolai maps in these sectors is given explicitly, and it is shown that they have a natural stochastic interpretation. This result also suggests a probabilistic interpretation of the wave function.