Path Integral and Spectral Representations for Supersymmetric Dirac-Hamiltonians
Quantum Physics
2018-05-11 v1 High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
The resolvent of supersymmetric Dirac Hamiltonian is studied in detail. Due to supersymmetry the squared Dirac Hamiltonian becomes block-diagonal whose elements are in essence non-relativistic Schr\"odinger-type Hamiltonians. This enables us to find a Feynman-type path-integral representation of the resulting Green's functions. In addition, we are also able to express the spectral properties of the supersymmetric Dirac Hamiltonian in terms of those of the non-relativistic Schr\"odinger Hamiltonians. The methods are explicitly applied to the free Dirac Hamiltonian, the so-called Dirac oscillator and a generalization of it. The general approach is applicable to systems with good and broken supersymmetry.
Cite
@article{arxiv.1712.08759,
title = {Path Integral and Spectral Representations for Supersymmetric Dirac-Hamiltonians},
author = {Georg Junker and Akira Inomata},
journal= {arXiv preprint arXiv:1712.08759},
year = {2018}
}
Comments
18 pages