Freedman's theorem for unitarily invariant states on the CCR algebra

DOI10.1007/s00220-024-04932-9arXiv2310.06691OpenAlexW4391678178MaRDI QIDQ6153515

Simone Del Vecchio, Stefano Rossi, Tommaso Monni, Vitonofrio Crismale

Publication date: 14 February 2024

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2310.06691

Mathematics Subject Classification ID

Applications of selfadjoint operator algebras to physics (46L60) States of selfadjoint operator algebras (46L30) Stochastic processes (60Gxx) Miscellaneous applications of functional analysis (46Nxx)

Cites Work

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• De Finetti theorem on the CAR algebra
• Primitive ideals in enveloping algebras
• Nonregular representations of CCR algebras and algebraic fermion bosonization
• Wick order, spreadability and exchangeability for monotone commutation relations
• On the monotone \(C^\ast \)-algebra
• Exchangeable stochastic processes and symmetric states in quantum probability
• Quasi-free states of the C.C.R.-algebra and Bogoliubov transformations
• Symmetric states of infinite tensor products of \(C^ *\)-algebras
• Tail algebras for monotone and \(q\)-deformed exchangeable stochastic processes
• Markov property of Gaussian states of canonical commutation relation algebras
• Quantum rotatability
• Invariants Under Mixing which Generalize de Finetti's Theorem
• Probabilistic Symmetries and Invariance Principles
• De Finetti-type theorems on quasi-local algebras and infinite Fermi tensor products

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