October 2011
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Day October 7, 2011

PT-symmetric quantum models living in an auxiliary Pontryagin space

Miloslav Znojil

An extension of the scope of quantum theory is proposed in a way inspired by the recent heuristic as well as phenomenological success of the use of non-Hermitian Hamiltonians which are merely required self-adjoint in a Krein space with an indefinite metric (chosen, usually, as the operator of parity). In nuce, the parity-like operators are admitted to represent the mere indefinite metric in a Pontryagin space. A constructive version of such a generalized quantization strategy is outlined and, via a non-numerical illustrative example, found feasible.

http://arxiv.org/abs/1110.1218
Mathematical Physics (math-ph)