Self-adjoint extensions and SUSY breaking in Supersymmetric Quantum Mechanics

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.

LaTeX. 23 pages and 1 figure (minor changes). Version to appear in the Journal of Physics A: Mat. and Gen

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