Hilbert Space Structures on the Solution Space of Klein-Gordon Type Evolution Equations
Mathematical Physics
2017-08-23 v3 General Relativity and Quantum Cosmology
High Energy Physics - Theory
math.MP
Quantum Physics
Abstract
We use the theory of pseudo-Hermitian operators to address the problem of the construction and classification of positive-definite invariant inner-products on the space of solutions of a Klein-Gordon type evolution equation. This involves dealing with the peculiarities of formulating a unitary quantum dynamics in a Hilbert space with a time-dependent inner product. We apply our general results to obtain possible Hilbert space structures on the solution space of the equation of motion for a classical simple harmonic oscillator, a free Klein-Gordon equation, and the Wheeler-DeWitt equation for the FRW-massive-real-scalar-field models.
Cite
@article{arxiv.math-ph/0209014,
title = {Hilbert Space Structures on the Solution Space of Klein-Gordon Type Evolution Equations},
author = {Ali Mostafazadeh},
journal= {arXiv preprint arXiv:math-ph/0209014},
year = {2017}
}
Comments
29 pages, slightly revised version, accepted for publication in Class. Quantum Grav