The Dirac Operator in a Fermion Bag Background in 1+1 Dimensions and Generalized Supersymmetric Quantum Mechanics

TL;DR

This paper explores the spectral properties of the Dirac operator in a static background in 1+1 dimensions, revealing a connection to a generalized form of supersymmetric quantum mechanics and its implications.

Contribution

It introduces a novel generalization of supersymmetric quantum mechanics to analyze the Dirac operator in a fermion bag background in 1+1 dimensions.

Findings

Spectral theory of the Dirac operator is linked to generalized supersymmetric quantum mechanics.

The approach provides new insights into the structure of fermion bag backgrounds.

Potential applications in understanding low-dimensional quantum field theories.

Abstract

We show that the spectral theory of the Dirac operator $D = i\delsl-\sigma(x) -i\pi(x)\gam_5$ in a static background $(\sigma(x),\pi(x))$ in 1+1 space-time dimensions, is underlined by a certain generalization of supersymmetric quantum mechanics, and explore its consequences.