Title: Existence and structure of infinitely degenerate zero-energy ground states of a Wess–Zumino-type model in supersymmetric quantum mechanics
Abstract:It is known that the N=2 Wess–Zumino supersymmetric quantum mechanical model with the superpotential V(z)=λeαz(λ ∈ C\{0},α≥0) has infinitely many bosonic zero-energy ground states and no fermionic zer...It is known that the N=2 Wess–Zumino supersymmetric quantum mechanical model with the superpotential V(z)=λeαz(λ ∈ C\{0},α≥0) has infinitely many bosonic zero-energy ground states and no fermionic zero-energy ground states [A. Arai, J. Math. Phys. 30, 1164 (1989)]. In this article, these results are extended to a more general model. The main results include the following: (1) identification of the spectra of the Hamiltonian H of the model; (2) non-Fredholmness of a supercharge of the model, which is a Dirac-type operator; (3) existence of infinitely many bosonic zero-energy states of H; (4) nonexistence of fermionic zero-energy states of H.Read More