PT-symmetric quantum models living in an auxiliary Pontryagin space

TL;DR

This paper proposes a new extension of quantum theory using PT-symmetric models in Pontryagin spaces, broadening the mathematical framework for non-Hermitian Hamiltonians with indefinite metrics.

Contribution

It introduces a constructive approach to quantization in Pontryagin spaces, expanding the mathematical foundation for PT-symmetric quantum models.

Findings

Feasibility demonstrated through a non-numerical example

Extends quantum theory to include indefinite metric spaces

Provides a constructive quantization method

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.