Classical analog of extended phase space SUSY and its breaking

TL;DR

This paper develops a classical analog of extended phase space supersymmetric quantum mechanics, analyzes SUSY breaking mechanisms, and explores algebraic properties related to shape invariance and tunneling effects.

Contribution

It introduces a classical analog of extended phase space SUSY, derives approximate groundstate solutions, and investigates non-perturbative SUSY breaking via instantons.

Findings

Groundstate energy as a SUSY breaking measure

Expectation value of auxiliary field as a practical SUSY breaking indicator

Non-perturbative tunneling effects cause SUSY breaking

Abstract

We derive the classical analog of the extended phase space quantum mechanics of the particle with odd degrees of freedom which gives rise to (N=2)-realization of supersymmetry (SUSY) algebra. By means of an iterative procedure, we find the approximate groundstate solutions to the extended Schr\"{o}dinger-like equation and use these solutions further to calculate the parameters which measure the breaking of extended SUSY such as the groundstate energy. Consequently, we calculate a more practical measure for the SUSY breaking which is the expectation value of an auxiliary field. We analyze non-perturbative mechanism for extended phase space SUSY breaking in the instanton picture and show that this has resulted from tunneling between the classical vacua of the theory. Particular attention is given to the algebraic properties of shape invariance and spectrum generating algebra.