Ali Mostafazadeh 2003 Class. Quantum Grav. 20 155 doi:10.1088/0264-9381/20/1/312
Ali Mostafazadeh
Show affiliationsWe 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.
47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)
47A70 (Generalized) eigenfunction expansions; rigged Hilbert spaces
Issue 1 (7 January 2003)
Received 27 September 2002
Published 12 December 2002
Ali Mostafazadeh 2003 Class. Quantum Grav. 20 155
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