Classical limits of unbounded quantities by strict quantization. (English) Zbl 1454.81081

Summary: This paper extends the tools of \(C^*\)-algebraic strict quantization toward analyzing the classical limits of unbounded quantities in quantum theories. We introduce the approach first in the simple case of finite systems. Then, we apply this approach to analyze the classical limits of unbounded quantities in bosonic quantum field theories, with particular attention to number operators and Hamiltonians. The methods take classical limits in a representation-independent manner and so allow one to compare quantities appearing in inequivalent Fock space representations.
©2020 American Institute of Physics


81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
81V73 Bosonic systems in quantum theory
81T70 Quantization in field theory; cohomological methods
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
30H20 Bergman spaces and Fock spaces
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