A \(C^*\)-dynamical system with Dedekind zeta partition function and spontaneous symmetry breaking

DOI10.5802/jtnb.236zbMath0962.11031OpenAlexW1967603663MaRDI QIDQ1809037

Paula Beazley Cohen

Publication date: 7 February 2000

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=JTNB_1999__11_1_15_0

zbMATH Keywords

Riemann zeta functionquantum theorypartition functionDedekind zeta functionRiemann hypothesisspontaneous symmetry breaking\(C^*\)-dynamical systemquantum statistical mechanicsBost-Connes theory

Mathematics Subject Classification ID

Noncommutative dynamical systems (46L55) Symmetry breaking in quantum theory (81R40) Quantum dynamics and nonequilibrium statistical mechanics (general) (82C10) Other Dirichlet series and zeta functions (11M41) Miscellaneous applications of number theory (11Z05)

Related Items (4)

Cyclotomy and Ramanujan sums in quantum phase locking ⋮ Constructing number field isomorphisms from \(*\)-isomorphisms of certain crossed product \(\mathrm{C}^*\)-algebras ⋮ Bost-Connes type systems for function fields ⋮ Partial crossed product description of the 𝐶*-algebras associated with integral domains

Cites Work

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• Extension of spontaneous symmetry breaking of Bost-Connes in case of arbitrary global fields
• Semigroups of *-endomorphisms, Dirichlet series, and phase transitions
• Semigroup crossed products and Hecke algebras arising from number fields
• Hecke algebras, type III factors and phase transitions with spontaneous symmetry breaking in number theory
• Semigroup crossed products and the Toeplitz algebras of nonabelian groups
• A Semigroup Crossed Product Arising in Number Theory

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