Operator integrals and phase space observables



: Lahti P, Pellonpaa JP, Ylinen K

Publisher: AMER INST PHYSICS

: 1999

Journal of Mathematical Physics

JOURNAL OF MATHEMATICAL PHYSICS

: J MATH PHYS

: 40

: 4

: 2181

: 2189

: 9

: 0022-2488

DOI: https://doi.org/10.1063/1.532858


The operator integral integral f dE of a complex valued measurable function f with respect to a positive operator measure E is considered. If F is a Neumark dilation of E into a projection measure, then the "projected'' operator integral pr(integral fdF) is a restriction of the operator integral f dE. Necessary and sufficient conditions for the equality pr( integral f dF) = integral f dE are obtained. The results are applied to determine the moment operators of the phase space observables generated by the number states. (C) 1999 American Institute of Physics. [S0022-2488(99)01104-4].



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