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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.

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Related: – Qmechanic Apr 9 '14 at 23:54

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Prof. Arai Asao published monographs that include mathematically rigorous treatment of SUSY which seem to be your posted subject. However those are written in Japanese. Arai published several research papers on which some parts of those monographs are based. I think these journal papers can be used for pedagogic purposes if you have some familiarity with functional analysis.

Arai, Asao On self-adjointness of Dirac operators in boson-fermion Fock spaces.
Hokkaido Math. J. 23 (1994), no. 2, 319–353.
It is available from

Arai, Asao(J-HOKK) A general class of infinite-dimensional Dirac operators and path integral representation of their index. J. Funct. Anal. 105 (1992), no. 2, 342–408.

The Dirac Equation (Texts and Monographs in Physics)
by Prof.Bernd Thaller seems to include some relevant information, though its title is not SUSY itself.

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