Partial Differential Equations and Quantum States in Curved Spacetimes
| Autor: | Matteo Capoferri, Zhirayr Avetisyan |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
General Mathematics
WICK POLYNOMIALS HADAMARD STATES MICROLOCAL SPECTRUM CONDITION Quantum state Computer Science (miscellaneous) partial differential equations QA1-939 THEOREM 2-POINT FUNCTION Quantum field theory TIME ORDERED PRODUCTS Engineering (miscellaneous) quantum field theory Mathematical physics Physics Partial differential equation CONSTRUCTION Spacetime SINGULARITY STRUCTURE Propagator hyperbolic propagators Riemannian manifold OPERATOR FIELD-THEORY Mathematics and Statistics Physics and Astronomy Cotangent bundle Hadamard states Distribution (differential geometry) Mathematics |
| Zdroj: | Mathematics, Vol 9, Iss 1936, p 1936 (2021) MATHEMATICS |
| ISSN: | 2227-7390 |
| Popis: | In this review paper, we discuss the relation between recent advances in the theory of partial differential equations and their applications to quantum field theory on curved spacetimes. In particular, we focus on hyperbolic propagators and the role they play in the construction of physically admissible quantum states—the so-called Hadamard states—on globally hyperbolic spacetimes. We will review the notion of a propagator and discuss how it can be constructed in an explicit and invariant fashion, first on a Riemannian manifold and then on a Lorentzian spacetime. Finally, we will recall the notion of Hadamard state and relate the latter to hyperbolic propagators via the wavefront set, a subset of the cotangent bundle capturing the information about the singularities of a distribution. |
| Databáze: | OpenAIRE |
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