How quantum mechanics probes superspace

TL;DR

This paper explores how supersymmetric quantum theories can unify different descriptions of particle fluctuations, linking non-relativistic particle partition functions with superspace concepts, and providing testable identities for these relations.

Contribution

It demonstrates that the partition functions from different fluctuation models are connected through an ${\mathcal N}=1$ supersymmetric framework, offering a unified description of particle fluctuations.

Findings

Partition functions from Langevin and equilibrium models are related via supersymmetry.

Correlation functions satisfy identical identities across models, confirming the unified description.

Supersymmetry provides a consistent closure even when broken by backreaction effects.

Abstract

We study the relation between the partition function of a non--relativistic particle, that describes the equilibrium fluctuations implicitly, and the partition function of the same system, deduced from the Langevin equation, that describes the fluctuations explicitly, of a bath with additive white--noise properties. We show that both can be related to the partition function of an ${\mathcal N}=1$ supersymmetric theory with one--dimensional bosonic worldvolume and that they can all describe the same physics, since the correlation functions of the observables satisfy the same identities for all systems.The supersymmetric theory provides the consistent closure for describing the fluctuations, even though supersymmetry may be broken, when their backreaction is taken into account. The trajectory of the classical particle becomes a component of a superfield, when fluctuations are taken into account. These statements can be tested by the identities the correlation functions satisfy, by using a lattice regularization of an action that describes commuting fields only.