Meromorphic N=2 Wess–Zumino supersymmetric quantum mechanics
- 1 September 1991
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 32 (9), 2427-2434
- https://doi.org/10.1063/1.529170
Abstract
The ordinary (holomorphic) N=2 Wess–Zumino model in supersymmetric quantum mechanics is extended to the case where the superpotential V(z) is a meromorphic function on C■{∞}. The extended model is analyzed in a mathematically rigorous way. Self‐adjoint extensions and the essential self‐adjointness of the supercharges are discussed. The supersymmetric Hamiltonian defined by one of the self‐adjoint extensions of the supercharges has no fermionic zero‐energy states (‘‘vanishing theorem’’). It is proven that if V(z) has only one pole at z=0 in C, then the supercharges are essentially self‐adjoint on C∞0(R2■{0};C4). The special case where V(z)=λz−p(p∈N,λ∈C■{0}) is analyzed in detail to prove the following facts: (i) the number of the bosonic zero‐energy ground state(s) is equal to p−1; (ii) the supercharges are not Fredholm.Keywords
This publication has 7 references indexed in Scilit:
- Symmetries and ground states of N = 2 SUSY Wess-Zumino quantum mechanicsAnnals of Physics, 1990
- On the degeneracy in the ground state of the N=2 Wess–Zumino supersymmetric quantum mechanicsJournal of Mathematical Physics, 1989
- Existence of infinitely many zero-energy states in a model of supersymmetric quantum mechanicsJournal of Mathematical Physics, 1989
- Ground state structure in supersymmetric quantum mechanicsAnnals of Physics, 1987
- Some remarks on scattering theory in supersymmetric quantum systemsJournal of Mathematical Physics, 1987
- Supersymmetry and singular perturbationsJournal of Functional Analysis, 1985
- Supersymmetry and Morse theoryJournal of Differential Geometry, 1982