PT-symmetric quantum models living in an auxiliary Pontryagin space
arXiv:1110.1218
Abstract
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.
14 pp., 2 figs., extended version of a part of the contributed talk to the int. conf. IWOTA 2010 (Technische Universität Berlin, Germany, July 12th-16th, 2010), cf. http://www3.math.tu-berlin.de/iwota_2010