Applications of Partial Supersymmetry

Details Applications of Partial Supersymmetry Applications of Partial Supersymmetry

2003-10-23

arxiv.org/abs/quant-ph/0310149v2

J.Phys.A37:4861-4870,2004

Physics

Quantum Physics

11 pages, harvmac, no figures; typo corrected in identifying info on title page

Scientific paper

10.1088/0305-4470/37/17/015

I examine quantum mechanical Hamiltonians with partial supersymmetry, and explore two main applications. First, I analyze a theory with a logarithmic spectrum, and show how to use partial supersymmetry to reveal the underlying structure of this theory. This method reveals an intriguing equivalence between two formulations of this theory, one of which is one-dimensional, and the other of which is infinite-dimensional. Second, I demonstrate the use of partial supersymmetry as a tool to obtain the asymptotic energy levels in non-relativistic quantum mechanics in an exceptionally easy way. In the end, I discuss possible extensions of this work, including the possible connections between partial supersymmetry and renormalization group arguments.

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