Self-adjoint extensions and SUSY breaking in Supersymmetric Quantum Mechanics

Details Self-adjoint extensions and SUSY breaking in Supersymmetric Quantum Mechanics Self-adjoint extensions and SUSY breaking in Supersymmetric Quantum Mechanics

2005-01-11

arxiv.org/abs/hep-th/0501083v2

J.Phys.A38:4665-4683,2005

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1088/0305-4470/38/21/011

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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