Path integrals on a flux cone

TL;DR

This paper derives the quantum propagator on a flux cone with a magnetic flux at the conical singularity, using operator formalism and path integrals, revealing natural quantum corrections without assuming space connectivity.

Contribution

It provides a novel derivation of the Schrödinger propagator on a flux cone using combined operator and path integral methods, including quantum corrections.

Findings

Explicit path integral representation of the propagator

Quantum corrections emerge naturally in the Lagrangian

No assumptions about the connectivity of the configuration space

Abstract

This paper considers the Schroedinger propagator on a cone with the conical singularity carrying magnetic flux (``flux cone''). Starting from the operator formalism and then combining techniques of path integration in polar coordinates and in spaces with constraints, the propagator and its path integral representation are derived. "Quantum correction" in the Lagrangian appears naturally and no a priori assumption is made about connectivity of the configuration space.