Extended SUSY quantum mechanics: transition amplitudes and path integrals

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.

1+26 pages

References in corpus (5)

• Detours and Paths: BRST Complexes and Worldline Formalism
• U(N) spinning particles and higher spin equations on complex manifolds
• Supersymmetric Quantum Mechanics and Super-Lichnerowicz Algebras
• Half-integer Higher Spin Fields in (A)dS from Spinning Particle Models
• U(N|M) quantum mechanics on Kaehler manifolds

Cited by in corpus (17)

• Light bending from eikonal in worldline quantum field theory
• Effective action for higher spin fields on (A)dS backgrounds
• Quantum mechanical path integrals in the first quantised approach to quantum field theory
• One-loop quantum gravity from the N=4 spinning particle
• Quantum theories of (p,q)-forms
• Quantum theory of massless (p,0)-forms
• Worldline description of a bi-adjoint scalar and the zeroth copy
• Massive and massless higher spinning particles in odd dimensions
• Mixed symmetry Wilson-loop interactions in the worldline formalism
• Six-dimensional one-loop divergences in quantum gravity from the $\mathcal{N}=4$ spinning particle
• Quantum mechanical path integrals in curved spaces and the type-A trace anomaly
• Gauge-invariant coefficients in perturbative quantum gravity
• Path integral calculation of heat kernel traces with first order operator insertions
• Simplified path integral for supersymmetric quantum mechanics and type-A trace anomalies
• One-loop quantum gravity from a worldline viewpoint
• On the simplified path integral on spheres
• U(N) spinning particles and higher spin fields on Kaehler backgrounds