Hilbert Space Structures on the Solution Space of Klein-Gordon Type Evolution Equations
数学物理
2017-08-23 v3 广义相对论与量子宇宙学
高能物理 - 理论
math.MP
量子物理
摘要
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.
引用
@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}
}
备注
29 pages, slightly revised version, accepted for publication in Class. Quantum Grav