Supersymmetry and the Dirac equation

Journal Article · Sat Oct 01 04:00:00 EDT 1988 · Ann. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1016/0003-4916(88)90279-5· OSTI ID:6607865

Copper, F; Khare, A; Musto, R; Wipf, A

We discuss in detail two supersymmetries of the 4-dimensional Dirac operator D-italic-dash-bar/sup 2/ where D-italic-dash-bar = partial-dash-bar-ieA-italic-dash-bar, 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 D-italic-dash-bar/sup 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 Schroedinger 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/sup 2/(x)+phi''(x). We also discussed and exploit the supersymmetry of the path integral representation for the fermion propagator in an external field. copyright 1988 Academic Press, Inc.

• Research Organization: Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
• OSTI ID: 6607865
• Journal Information: Ann. Phys. (N.Y.); (United States), Journal Name: Ann. Phys. (N.Y.); (United States) Vol. 187:1; ISSN APNYA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANALYTICAL SOLUTION
CHIRALITY
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
DYNAMICAL GROUPS
EIGENFUNCTIONS
ENERGY SPECTRA
EQUATIONS
FOUR-DIMENSIONAL CALCULATIONS
FUNCTIONS
LIE GROUPS
MATHEMATICAL OPERATORS
MATRICES
O GROUPS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE PROPERTIES
QUANTUM OPERATORS
S MATRIX
SCHROEDINGER EQUATION
SPECTRA
SU GROUPS
SU-2 GROUPS
SUPERSYMMETRY
SYMMETRY
SYMMETRY GROUPS
WAVE EQUATIONS