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Hilbert Space Structures on the Solution Space of Klein-Gordon Type Evolution Equations

Ali Mostafazadeh
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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.

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Ali Mostafazadeh. 2002-11-28. Hilbert Space Structures on the Solution Space of Klein-Gordon Type Evolution Equations. https://doi.org/10.1088/0264-9381%2F20%2F1%2F312

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