PT-symmetric quantum models living in an auxiliary Pontryagin space

Details PT-symmetric quantum models living in an auxiliary Pontryagin space PT-symmetric quantum models living in an auxiliary Pontryagin space

2011-10-06

arxiv.org/abs/1110.1218v1

Physics

Mathematical Physics

14 pp., 2 figs., extended version of a part of the contributed talk to the int. conf. IWOTA 2010 (Technische Universit\"at Ber

Scientific paper

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.

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