Path Integral and Spectral Representations for Supersymmetric Dirac-Hamiltonians

Autor:	Junker, Georg, Inomata, Akira
Rok vydání:	2017
Předmět:	Quantum Physics High Energy Physics - Theory Mathematical Physics 03.65.Pm Relativistic wave equations 11.30.Pb Supersymmetry
Zdroj:	Journal of Mathematical Physics 59, 052301 (2018)
Druh dokumentu:	Working Paper
DOI:	10.1063/1.5020545
Popis:	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. Comment: 18 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1712.08759 Zobrazit plný text záznamu View this record from Arxiv