Extended SUSY quantum mechanics: transition amplitudes and path integrals

TL;DR

This paper explores extended supersymmetric quantum mechanics models, calculating transition amplitudes and heat kernels using various regularization schemes to ensure scheme independence, with applications to higher spin fields in curved backgrounds.

Contribution

It introduces a detailed perturbative calculation of transition amplitudes in extended SUSY quantum mechanics with multiple regularization schemes and identifies counterterms for scheme independence.

Findings

Explicit heat kernel calculations for extended SUSY models.

Identification of counterterms for different regularization schemes.

Application to higher spin fields on curved backgrounds.

Abstract

Quantum mechanical models with extended supersymmetry find interesting applications in worldline approaches to relativistic field theories. In this paper we consider one-dimensional nonlinear sigma models with O(N) extended supersymmetry on the worldline, which are used in the study of higher spin fields on curved backgrounds. We calculate the transition amplitude for euclidean times (i.e. the heat kernel) in a perturbative expansion, using both canonical methods and path integrals. The latter are constructed using three different regularization schemes, and the corresponding counterterms that ensure scheme independence are explicitly identified.