Miloslav Znojil, Hendrik B. Geyer

A new version of PT-symmetric quantum theory is proposed and illustrated by an N-site-lattice Legendre oscillator. The essence of the innovation lies in the replacement of parity P (serving as an indefinite metric in an auxiliary Krein space) by its non-involutory alternative P(positive)=Q>0 playing the role of a positive-definite nontrivial metric in an auxiliary, redundant, unphysical Hilbert space. It is shown that the QT-symmetry of this form remains appealing and technically useful.

http://arxiv.org/abs/1201.5058

Quantum Physics (quant-ph)