The microlocal spectrum condition and Wick polynomials of free fields on curved spacetimes

DOI10.1007/BF02099626zbMath0923.58052arXivgr-qc/9510056OpenAlexW2003470918MaRDI QIDQ1924103

Yanyan Li

Publication date: 31 October 1999

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

Full work available at URL: https://arxiv.org/abs/gr-qc/9510056

zbMATH Keywords

algebraic quantum field theorywave front setshyperbolic spacetime\(m\)-point distributions

Mathematics Subject Classification ID

Quantum field theory on curved space or space-time backgrounds (81T20) Axiomatic quantum field theory; operator algebras (81T05) Methods of quantum field theory in general relativity and gravitational theory (83C47) Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs (35A27) Propagation of singularities; initial value problems on manifolds (58J47)

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Cites Work

• 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
• Algebras of local observables on a manifold
• 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
• Fourier integral operators. I
• Fourier integral operators. II
• Dirac Quantum Fields on a Manifold
• QUANTIZED ELECTROMAGNETIC FIELD ON A MANIFOLD
• New examples for Wightman fields on a manifold
• On structure of the algebra of field operators
• An Algebraic Approach to Quantum Field Theory
• Curvature structures and conformal transformations
• On the discrete time matrix Riccati equation of optimal control†

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