Mathematical Physics SUSY QM Resource Recommendation

Question

I want to study SUSY QM. I found some excellent physically motivated articles on Arxiv. Despite, I am especially interested in the mathematical structure behind SUSY QM. Does anybody know whether there is a particularly good reference to start studying SUSY QM from a rigorous mathematical point of view. The reference should cover Spectral analysis and a wide range of all the algebraic properties concerned with the topic.

This post imported from StackExchange Physics at 2014-04-13 14:33 (UCT), posted by SE-user Lipschitz

Comments

Related: physics.stackexchange.com/q/28880/2451

This post imported from StackExchange Physics at 2014-04-13 14:33 (UCT), posted by SE-user Qmechanic

Answer 1

The original article is still among the best:

• Edward Witten, Supersymmetry and Morse theory J. Differential Geom. Volume 17, Number 4 (1982), 661-692. (Euclid, pdf, spire)

But I would suggest to start with this one here

• Jürg Fröhlich, Oiver Grandjean, Andreas Recknagel, Supersymmetric quantum theory, non-commutative geometry, and gravitation Lecture Notes Les Houches (1995) (arXiv:hep-th/9706132).

and read Witten in parallel.

For more see the references listed here

Answer 2

If you are just interested in the quantum mechanics of SUSY (rather than its quantum field theory), you should read the comprehensive (though now 20 years old and no longer fully up to date) survey article 

F. Cooper, A. Khare, U. Sukhatme,
Supersymmetry and quantum mechanics,
Physics Reports 251 (1995), 267-385.
http://jensen.thphys.uni-heidelberg.de/~maniatis/LectureAdv/SusyQM.pdf

The math is straightforward analysis of ODEs, so no special safeguards are needed.