Abstract
Some relationships between two differentconcepts of noncommutative time operators are discussed.One is the concept of a Hermitian, but not self-adjointtime operator TB based on apositive-operator-valued measure for a dynamical observable B. The otheris the concept of a self-adjoint time operatorTL obtained in the Liouville representation,a special case of the standard representation of quantumtheory. Conditions are indicated under which aself-adjoint extension of TB leading toTL can be constructed. Similarities with thenotions of consistent and inconsistent histories areindicated. Conceptual issues as to the interpretation of the different timeoperators are outlined with particular emphasis on thenotion of temporal nonlocality.
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Atmanspacher, H., Amann, A. Positive-Operator-Valued Measures and Projection-Valued Measures of Noncommutative Time Operators. International Journal of Theoretical Physics 37, 629–650 (1998). https://doi.org/10.1023/A:1026604126629
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DOI: https://doi.org/10.1023/A:1026604126629