An Introduction To The Mathematical Structure Of Quantum Mechanics

By F. Strocchi. 2008

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Quantum Mechanics for Mathematicians (2008, methodology): “For a brief review of integration theory, including the Riesz-Markov theorem, see [RS80]; for the proof of the Gelfand-Naimark theorem and more details on C⇤-algebras, see [Str05] and references therein.”
Algebraic QFT in Curved Spacetime and Quasifree Hadamard States: An Introduction (2014, background): “The justification of a linear structure for the set of the observables is quite easy, the presence of an associative product is instead much more difficult to justify [61].”
Quantum-enhanced measurements without entanglement (2017, background): “…view usually adopted in the analysis of many-body systems, for which the primary object of investigation are the algebras of operators rather than their representations on particular Hilbert spaces (Bratteli and Robinson, 1987; Emch, 1972; Haag, 1992; Strocchi, 1985, 2008a,b, 2012; Thirring, 2002).”
Markovianity and non-Markovianity in quantum and classical systems (2011, background): “On the one hand, to make statements about the value of a certain observable at different times, a measurement scheme has to be specified which affects the subsequent time evolution; on the other, the statistical operator of a quantum system provides different, and generally incompatible, classical p”