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Self-adjoint extensions and SUSY breaking in Supersymmetric Quantum Mechanics

H. Falomir·P. A. G. Pisani
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Abstract

We consider the self-adjoint extensions (SAE) of the symmetric supercharges and Hamiltonian for a model of SUSY Quantum Mechanics in $\mathbb{R}^+$ with a singular superpotential. We show that only for two particular SAE, whose domains are scale invariant, the algebra of N=2 SUSY is realized, one with manifest SUSY and the other with spontaneously broken SUSY. Otherwise, only the N=1 SUSY algebra is obtained, with spontaneously broken SUSY and non degenerate energy spectrum.

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H. Falomir, P. A. G. Pisani. 2005-04-13. Self-adjoint extensions and SUSY breaking in Supersymmetric Quantum Mechanics. https://doi.org/10.1088/0305-4470%2F38%2F21%2F011

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