Aspects of supersymmetric quantum mechanics

✍ Scribed by Fred Cooper; Barry Freedman

• Publisher: Elsevier Science
• Year: 1983
• Tongue: English
• Weight: 995 KB
• Volume: 146
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1016/0003-4916(83)90034-9

✦ Synopsis

We review the properties of supersymmetric quantum mechanics for a class of models proposed by Witten. Using both Hamiltonian and path integral formulations, we give general conditions for which supersymmetry is broken (unbroken) by quantum fluctuations. The spectrum of states is discussed, and a virial theorem is derived for the energy. We also show that the euclidean path integral for supersymmetric quantum mechanics is equivalent to a classical stochastic process when the supersymmetry is unbroken (E, = 0). By solving a Fokker-Planck equation for the classical probability distribution, we find P,(y) is identical to 1 YO(~)l' in the quantum theory.