期刊
CLASSICAL AND QUANTUM GRAVITY
卷 20, 期 1, 页码 155-171出版社
IOP PUBLISHING LTD
DOI: 10.1088/0264-9381/20/1/312
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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.
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