Supersymmetry and the Dirac equation
type: Item
instance of: scholarly article
title: Supersymmetry and the Dirac equation
zbMATH Open document ID: 0651.58009
DOI: 10.1016/0003-4916(88)90279-5
author: Fred Cooper
author: Avinash Khare
author: R. Musto
author: Andreas Wipf
published in: Annals of Physics
publication date: 1988-01-01T00:00:00Z
review text: We discuss in detail two supersymmetries of the 4-dimensional Dirac operator \({\mathbb{D}}^ 2 \)where \({\mathbb{D}}=\partial -ieA\), namely the usual chiral supersymmetry and a separate complex supersymmetry. Using SUSY methods developed to categorize solvable potentials in 1-dimensional quantum mechanics we systematically study the cases where the spectrum, eigenfunctions, and S-matrix of \({\mathbb{D}}^ 2 \)can be obtained analytically. We relate these solutions to the solutions of the ordinary massive Dirac equation in external fields. We show that whenever a Schrödinger equation for a potential V(x) is exactly solvable, then there always exists a corresponding static scalar field \(\phi\) (x) for which the Jackiw-Rebbi type \((1+1)\)-dimensional Dirac equation is exactly solvable with V(x) and \(\phi\) (x) being related by \(V(x)=\phi\) \(2(x)+\phi '(x)\). We also discuss and exploit the supersymmetry of the path integral representation for the fermion propagator in an external field.
Mathematics Subject Classification ID: 58C50
Mathematics Subject Classification ID: 58J90
Mathematics Subject Classification ID: 81T60
Mathematics Subject Classification ID: 35Q99
zbMATH DE Number: 4062187
zbMATH Keywords: supersymmetries of the 4-dimensional Dirac operator
zbMATH Keywords: SUSY methods
zbMATH Keywords: Schrödinger equation
MaRDI profile type: Publication
full work available at URL: 0003-4916(88)90279-5
OpenAlex ID: W2047435412
cites work: On Gauge Invariance and Vacuum Polarization
cites work: Supersymmetry and the Atiyah-Singer index theorem
cites work: Theory of the Fermi Interaction
description: scientific article; zbMATH DE number 4062187