Notes for a quantum index theorem

DOI10.1007/s002200100492zbMath0992.81046arXivmath/0003082OpenAlexW2070012154MaRDI QIDQ5953668

Roberto Longo

Publication date: 27 January 2002

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

Full work available at URL: https://arxiv.org/abs/math/0003082

zbMATH Keywords

noncommutative geometrysuperselection sectorblack-hole entropychemical potential for thermal statescohomologies supercharge operatorholomorphic dimensionKMS functional cocycleslocal quantum physicsquantum indexRoberts and Connes-Takesaki cohomologies

Mathematics Subject Classification ID

Black holes (83C57) Supersymmetric field theories in quantum mechanics (81T60) Axiomatic quantum field theory; operator algebras (81T05) Noncommutative geometry methods in quantum field theory (81T75) General theory of (C^*)-algebras (46L05) Quantum equilibrium statistical mechanics (general) (82B10) Quantum dynamics and nonequilibrium statistical mechanics (general) (82C10) Operator algebra methods applied to problems in quantum theory (81R15) Automorphisms of selfadjoint operator algebras (46L40)

Related Items (27)

Comment on the Bekenstein bound ⋮ Representations of conformal nets, universal \(C^*\)-algebras and \(K\)-theory ⋮ Topological sectors and a dichotomy in conformal field theory ⋮ KMS states and the chemical potential for disordered systems ⋮ Modular conjugation and the implementation of supersymmetry ⋮ Examples of odd index theorems ⋮ Relative entropy and curved spacetimes ⋮ Nuclearity and thermal states in conformal field theory ⋮ Non-equilibrium thermodynamics and conformal field theory ⋮ Free products in AQFT ⋮ The emergence of time ⋮ Modular conjugations in 2D conformal field theory and holographic bit threads ⋮ Loop groups and noncommutative geometry ⋮ Local-entire cyclic cocycles for graded quantum field nets ⋮ Asymptotic morphisms and superselection theory in the scaling limit ⋮ The \(K\)-homology of nets of \(C^\ast\)-algebras ⋮ Thermal states in conformal QFT. I ⋮ Algebraic supersymmetry: a case study ⋮ Super-KMS functionals for graded-local conformal nets ⋮ On Landauer's principle and bound for infinite systems ⋮ The \(C_0(X)\)-algebra of a net and index theory ⋮ From operator algebras to superconformal field theory ⋮ The principle of locality: Effectiveness, fate, and challenges ⋮ \(N=2\) superconformal nets ⋮ Spectral triples and the super-Virasoro algebra ⋮ Entropy distribution of localised states ⋮ Noncommutative spectral invariants and black hole entropy

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