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Geometric mean of states and transition amplitudes. (English) Zbl 1172.46044
Summary: The transition amplitude between square roots of states, which is an analogue of Hellinger integral in classical measure theory, is investigated in connection with operator-algebraic representation theory. A variational expression based on geometric mean of positive forms is utilized to obtain an approximation formula for transition amplitudes.

46L60 Applications of selfadjoint operator algebras to physics
46L53 Noncommutative probability and statistics
81R15 Operator algebra methods applied to problems in quantum theory
Full Text: DOI arXiv
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