A local-to-global singularity theorem for quantum field theory on curved space-time (with an appendix by Rainer Verch)

DOI10.1007/BF02101180zbMath0874.58079MaRDI QIDQ1924092

Marek J. Radzikowski

Publication date: 14 October 1997

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

zbMATH Keywords

quantum field theoryglobally hyperbolic spacetimefree scalar fieldclass \({\mathcal P}_{M,g}\) conditionglobal Hadamard conditionKay's conjecturelocal Hadamard conditionsingularity structure of the two point function

Mathematics Subject Classification ID

Quantum field theory on curved space or space-time backgrounds (81T20) PDEs in connection with quantum mechanics (35Q40) Axiomatic quantum field theory; operator algebras (81T05) Methods of quantum field theory in general relativity and gravitational theory (83C47) Pseudodifferential and Fourier integral operators on manifolds (58J40) Propagation of singularities; initial value problems on manifolds (58J47)

Related Items

Radiative observables for linearized gravity on asymptotically flat spacetimes and their boundary induced states, SPECTRAL GEOMETRY OF SPACETIME, Constructing Hadamard states via an extended Møller operator, The Casimir effect from the point of view of algebraic quantum field theory, Micro-local approach to the Hadamard condition in quantum field theory on curved space-time, On the adiabatic limit of Hadamard states, The holographic Hadamard condition on asymptotically anti-de Sitter spacetimes, A new class of fermionic projectors: Møller operators and mass oscillation properties, The quantization of Proca fields on globally hyperbolic spacetimes: Hadamard states and Møller operators, Paracausal deformations of Lorentzian metrics and Møller isomorphisms in algebraic quantum field theory, The Unruh state for massless fermions on Kerr spacetime and its Hadamard property, On the algebraic quantization of a massive scalar field in anti-de Sitter spacetime, Infrared problem for the Nelson model on static space-times, Thermal state with quadratic interaction, Approximate KMS states for scalar and spinor fields in Friedmann-Robertson-Walker spacetimes, Quantum out-states holographically induced by asymptotic flatness: invariance under spacetime symmetries, energy positivity and Hadamard property, Analytic Hadamard states, Calderón projectors and Wick rotation near analytic Cauchy surfaces, Continuity of Symplectically Adjoint Maps and the Algebraic Structure of Hadamard Vacuum Representations for Quantum Fields on Curved Spacetime, On the construction of Hartle-Hawking-Israel states across a static bifurcate Killing horizon, On the global Hadamard parametrix in QFT and the signed squared geodesic distance defined in domains larger than convex normal neighbourhoods, Quantum fields in curved spacetime, Quantum fields from global propagators on asymptotically Minkowski and extended de Sitter spacetimes, Quantum instability of the Cauchy horizon in Reissner–Nordström–deSitter spacetime, HADAMARD STATES FOR THE VECTOR POTENTIAL ON ASYMPTOTICALLY FLAT SPACETIMES, Local causal structures, Hadamard states and the principle of local covariance in quantum field theory, RENORMALIZED QUANTUM YANG–MILLS FIELDS IN CURVED SPACETIME, Algebraic QFT in Curved Spacetime and Quasifree Hadamard States: An Introduction, Hadamard States From Null Infinity, Distinguished quantum states in a class of cosmological spacetimes and their Hadamard property, The art of the state, Tunnelling processes for Hadamard states through a 2+1 dimensional black hole and Hawking radiation, The fermionic signature operator in De Sitter spacetime, The cosmological semiclassical Einstein equation as an infinite-dimensional dynamical system, THE EXTENDED ALGEBRA OF OBSERVABLES FOR DIRAC FIELDS AND THE TRACE ANOMALY OF THEIR STRESS-ENERGY TENSOR, Global wave parametrices on globally hyperbolic spacetimes, QUANTUM FIELD THEORY ON CURVED BACKGROUNDS — A PRIMER, Møller operators and Hadamard states for Dirac fields with MIT boundary conditions, Hadamard states for quantized Dirac fields on Lorentzian manifolds of bounded geometry

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Generally covariant quantum field theory and scaling limits
• Theorems on the uniqueness and thermal properties of stationary, nonsingular, quasifree states on spacetimes with a bifurcate Killing horizon
• Radiation damping in a gravitational field
• Propagateurs et commutateurs en relativité générale
• The back reaction effect in particle creation in curved spacetime
• Algebras of local observables on a manifold
• Singularity structure of the two-point function in quantum field theory in curved spacetime. II
• Singularity structure of the two-point function in quantum field theory in curved spacetime
• Local definiteness, primarity and quasiequivalence of quasifree Hadamard quantum states in curved spacetime
• Local quasiequivalence and adiabatic vacuum states
• Micro-local approach to the Hadamard condition in quantum field theory on curved space-time
• Fourier integral operators. II
• Can locally Hadamard quantum states have non-local singularities?
• Scalar quantum field in an external gravitational field
• Spaces of positive and negative frequency solutions of field equations in curved space–times. I. The Klein–Gordon equation in stationary space–times
• Sufficient conditions for quasifree states and an improved uniqueness theorem for quantum fields on space–times with horizons
• New examples for Wightman fields on a manifold
• THE PRINCIPLE OF LOCALITY AND QUANTUM FIELD THEORY ON (NON GLOBALLY HYPERBOLIC) CURVED SPACETIMES
• On structure of the algebra of field operators
• An Algebraic Approach to Quantum Field Theory
• The Large Scale Structure of Space-Time
• General Relativity
• Quantum Fields in Curved Space