open access

https://hdl.handle.net/2115/13676

Meromorphic N=2 Wess-Zumino supersymmetric quantum mechanics

英語

fredholm equation

1991-09

American Institute of Physics

Journal of Mathematical Physics

32(9)

2427-2434

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(R^2＼{0};C^4). 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.

学術雑誌論文

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Copyright © 1991 American Institute of Physics

0022-2488

1089-7658