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.

PACS numbers: 98.80.Hw, 04.60.m, 03.65.Pm, 03.65.Bz

Print publication: Issue 1 (7 January 2003)
Received 27 September 2002
Published 12 December 2002