A \(\mathrm{C}^*\)-algebraic approach to interacting quantum field theories

DOI10.1007/s00220-020-03700-9zbMath1447.81155arXiv1902.06062OpenAlexW3098369054MaRDI QIDQ2191166

Detlev Buchholz, Klaus Fredenhagen

Publication date: 24 June 2020

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

Full work available at URL: https://arxiv.org/abs/1902.06062

zbMATH Keywords

local quantum physicsHaag-Kastler axioms

Mathematics Subject Classification ID

Vertex operators; vertex operator algebras and related structures (17B69) Perturbative methods of renormalization applied to problems in quantum field theory (81T15) Quantum field theory on curved space or space-time backgrounds (81T20) NLS equations (nonlinear Schrödinger equations) (35Q55) Axiomatic quantum field theory; operator algebras (81T05) General theory of (C^*)-algebras (46L05) Applications of selfadjoint operator algebras to physics (46L60) Perturbation theories for operators and differential equations in quantum theory (81Q15) (S)-matrix theory, etc. in quantum theory (81U20) Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems (70S05) Monoidal categories, symmetric monoidal categories (18M05)

Related Items (14)

On the Cauchy problem for Friedrichs systems on globally hyperbolic manifolds with timelike boundary ⋮ Dynamical C*-algebras and kinetic perturbations ⋮ The metric nature of matter ⋮ Arrow of time and quantum physics ⋮ Spacelike deformations: higher-helicity fields from scalar fields ⋮ Classical dynamics, arrow of time, and genesis of the Heisenberg commutation relations ⋮ The unitary Master Ward Identity: time slice axiom, Noether's theorem and anomalies ⋮ Asymptotic measurement schemes for every observable of a quantum field theory ⋮ Intertwining operators for symmetric hyperbolic systems on globally hyperbolic manifolds ⋮ The master Ward identity for scalar QED ⋮ Completing the quantum formalism in a contextually objective framework ⋮ From path integrals to dynamical algebras: a macroscopic view of quantum physics ⋮ C*-algebraic approach to interacting quantum field theory: inclusion of Fermi fields ⋮ Causal Lie products of free fields and the emergence of quantum field theory

Cites Work

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• Mathematical aspects of quantum field theories. Contributions of the Les Houches winter school `Mathematical aspects of field theories', Les Houches, France, January and February 2012
• Construction of KMS states in perturbative QFT and renormalized Hamiltonian dynamics
• Perturbative algebraic quantum field theory and the renormalization groups
• Über die Multiplikation der Kausalfunktionen in der Quantentheorie der Felder
• Standard and split inclusions of von Neumann algebras
• Perturbative algebraic quantum field theory. An introduction for mathematicians
• Singularity structure of the two-point function in quantum field theory in curved spacetime. II
• The analysis of linear partial differential operators. I: Distribution theory and Fourier analysis.
• The generally covariant locality principle -- a new paradigm for local quantum field theory
• On the renormalization group in curved spacetime
• Microlocal analysis and interacting quantum field theories: renormalization on physical back\-grounds.
• Weak adiabatic limit in quantum field theories with massless particles
• The microlocal spectrum condition and Wick polynomials of free fields on curved spacetimes
• Batalin-Vilkovisky formalism in perturbative algebraic quantum field theory
• Superposition, transition probabilities and primitive observables in infinite quantum systems
• The quantum sine-Gordon model in perturbative AQFT
• Algebraic equivalence of locally normal representations
• Erratum to: ``The universal \(C^*\)-algebra of the electromagnetic field
• Existence of the Bogoliubov S(g) operator for the (:φ4:)2 quantum field theory
• CONSERVATION OF THE STRESS TENSOR IN PERTURBATIVE INTERACTING QUANTUM FIELD THEORY IN CURVED SPACETIMES
• An Algebraic Approach to Quantum Field Theory
• An algebraic spectrum condition

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