Supersymmetric quantum mechanics living on topologically nontrivial Riemann surfaces

Details Supersymmetric quantum mechanics living on topologically nontrivial Riemann surfaces Supersymmetric quantum mechanics living on topologically nontrivial Riemann surfaces

2009-04-15

arxiv.org/abs/0904.2294v1

Pramana - J. Phys. 73, 397 - 404 (2009)

Physics

Mathematical Physics

14pp

Scientific paper

Supersymmetric quantum mechanics is constructed in a new non-Hermitian representation. Firstly, the map between the partner operators $H^{(\pm)}$ is chosen antilinear. Secondly, both these components of a super-Hamiltonian ${\cal H}$ are defined along certain topologically nontrivial complex curves $r^{(\pm)}(x)$ which spread over several Riemann sheets of the wave function. The non-uniqueness of our choice of the map ${\cal T}$ between "tobogganic" partner curves $r^{(+)}(x)$ and $r^{(-)}(x)$ is emphasized.

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