Conservation of pseudo-norm in PT symmetric quantum mechanics

TL;DR

This paper extends Stone's theorem to PT symmetric quantum mechanics, demonstrating that wave function evolution is pseudo-unitary and their pseudo-norm remains conserved over time, even when symmetry is broken.

Contribution

It introduces a pseudo-norm framework for PT symmetric quantum mechanics and proves its invariance during evolution, including in broken symmetry regimes.

Findings

Pseudo-unitary evolution of wave functions.

Pseudo-norm remains conserved over time.

Conservation holds even in broken symmetry regimes.

Abstract

An extension of the Stone's theorem to PT symmetric, extended quantum mechanics must employ its pseudo-norm. We show that the evolution of the wave functions is then pseudo-unitary, and emphasize that their pseudo-norm remains time-independent even in the spontaneously broken symmetry regime where the energies themselves cease to be real.