Construction of KMS states in perturbative QFT and renormalized Hamiltonian dynamics

DOI10.1007/s00220-014-2141-7zbMath1305.82012arXiv1306.6519OpenAlexW2015611666MaRDI QIDQ462875

Falk Lindner, Klaus Fredenhagen

Publication date: 22 October 2014

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

Full work available at URL: https://arxiv.org/abs/1306.6519

zbMATH Keywords

Kubo-Martin-Schwinger conditionperturbative algebraic quantum field theoryquantum field theory at non-zero temperaturestatistical quantum field theory

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) Perturbative methods of renormalization applied to problems in quantum field theory (81T15) Axiomatic quantum field theory; operator algebras (81T05) Applications of selfadjoint operator algebras to physics (46L60) Quantum equilibrium statistical mechanics (general) (82B10) Operator algebra methods applied to problems in quantum theory (81R15) Statistical thermodynamics (82B30)

Related Items (19)

KMS-like properties of local equilibrium states in quantum field theory ⋮ The universal \(C^*\)-algebra of the electromagnetic field ⋮ Constructing Hadamard states via an extended Møller operator ⋮ Algebraic approach to Bose-Einstein condensation in relativistic quantum field theory: spontaneous symmetry breaking and the Goldstone theorem ⋮ On the stability of KMS states in perturbative algebraic quantum field theories ⋮ A statistical mechanical model for non-perturbative regimes ⋮ The star product in interacting quantum field theory ⋮ A \(\mathrm{C}^*\)-algebraic approach to interacting quantum field theories ⋮ Equilibrium states for the massive sine-Gordon theory in the Lorentzian signature ⋮ Perturbative algebraic quantum field theory on quantum spacetime: adiabatic and ultraviolet convergence ⋮ Linear stability of semiclassical theories of gravity ⋮ Quantum spacetime and the universe at the big bang, vanishing interactions and fading degrees of freedom ⋮ Thermal state with quadratic interaction ⋮ Weak adiabatic limit in quantum field theories with massless particles ⋮ Relative entropy and entropy production for equilibrium states in pAQFT ⋮ Quantum fields in curved spacetime ⋮ The generalised principle of perturbative agreement and the thermal mass ⋮ Thermal Equilibrium States for Quantum Fields on Non-commutative Spacetimes ⋮ Equilibrium states in thermal field theory and in algebraic quantum field theory

Cites Work

• 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
• The time slice axiom in perturbative quantum field theory on globally hyperbolic spacetimes
• Quasi-particles at finite temperatures
• Nonequilibrium dynamics of scalar fields in a thermal bath
• Quantum field theory on curved spacetimes. Concepts and mathematical foundations. Extended lecture notes of the compact course quantum field theory on curved spacetimes, Potsdam, Germany, October 2007
• Stability properties and the KMS condition
• Formal GNS construction and states in deformation quantization
• Local definiteness, primarity and quasiequivalence of quasifree Hadamard quantum states in curved spacetime
• The generally covariant locality principle -- a new paradigm for local quantum field theory
• Towards a relativistic KMS-condition
• Microlocal analysis and interacting quantum field theories: renormalization on physical back\-grounds.
• Thermal quantum fields with spatially cutoff interactions in 1+1 space--time dimensions
• Perturbation theory of Wightman functions
• Existence of local covariant time ordered products of quantum fields in curved spacetime
• Perturbative quantum field theory at positive temperatures: An axiomatic approach
• Relative Hamiltonian for faithful normal states of a von Neumann algebra
• Axioms for Euclidean Green's functions
• On the equilibrium states in quantum statistical mechanics
• Haag-Ruelle scattering theory in presence of massless particles
• Dynamics of Charged Particles and their Radiation Field
• A New Approach to Quantum-Statistical Mechanics
• Quantum statistics of fields and multiple production of mesons
• Brownian Motion of a Quantum Oscillator
• KMS, ETC.
• Unruh effect and the concept of temperature
• THERMAL QUANTUM FIELDS WITHOUT CUT-OFFS IN 1+1 SPACE-TIME DIMENSIONS
• Postulates of Quantum Field Theory
• Quelques Propriétés Générales De L'intégrale De Configuration D'un Système De Particules Avec Interaction
• Relativistic Quantum Theory for Finite Time Intervals
• Algebraic quantum field theory, perturbation theory, and the loop expansion
• Temperature independent renormalization of finite temperature field theory
• Local Wick polynomials and time ordered products of quantum fields in curved spacetime
• Asymptotic dynamics of thermal quantum fields
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