Supersymmetry in quantum mechanics with point interactions
Tomoaki Nagasawa, Makoto Sakamoto, Kazunori Takenaga
TL;DR
This paper explores how supersymmetry can be realized in one-dimensional quantum systems with point interactions, identifying compatible interactions, constructing models with supercharges, and discussing symmetry breaking and extensions.
Contribution
It introduces a class of point interactions compatible with supersymmetry and constructs N=2 supersymmetric models on a circle with point interactions and superpotential.
Findings
Identified point interactions compatible with supersymmetry
Constructed N=2 supersymmetric quantum models with point interactions
Discussed spontaneous supersymmetry breaking and higher N extensions
Abstract
We investigate supersymmetry in one-dimensional quantum mechanics with point interactions. We clarify a class of point interactions compatible with supersymmetry and present N=2 supersymmetric models on a circle with two point interactions as well as a superpotential. A hidden su(2) structure inherent in the system plays a crucial role to construct the N=2 supercharges. Spontaneous breaking of supersymmetry due to point interactions and an extension to higher N-extended supersymmetry are also discussed.
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