The well-posedness of the Cauchy problem for the Dirac operator on globally hyperbolic manifolds with timelike boundary

DOI10.25537/dm.2020v25.737-765zbMath1446.58009arXiv1806.06544OpenAlexW4300909809MaRDI QIDQ782490

Simone Murro, Nadine Große

Publication date: 27 July 2020

Published in: Documenta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.06544

zbMATH Keywords

initial-boundary value problemCauchy problemDirac operatorMIT-boundary conditions

Mathematics Subject Classification ID

Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) PDEs in connection with relativity and gravitational theory (35Q75) Initial-boundary value problems for first-order hyperbolic systems (35L50) Boundary value problems on manifolds (58J32) Hyperbolic equations on manifolds (58J45)

Related Items

On the Cauchy problem for Friedrichs systems on globally hyperbolic manifolds with timelike boundary, Paracausal deformations of Lorentzian metrics and Møller isomorphisms in algebraic quantum field theory, On the uniqueness of invariant states, Intertwining operators for symmetric hyperbolic systems on globally hyperbolic manifolds, Fundamental solutions for the wave operator on static Lorentzian manifolds with timelike boundary, Møller operators and Hadamard states for Dirac fields with MIT boundary conditions

Cites Work

• Unnamed Item
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• Topological censorship for Kaluza-Klein space-times
• Self-adjointness of the Dirac Hamiltonian for a class of non-uniformly elliptic boundary value problems
• Wave equations on Lorentzian manifolds and quantization.
• The Dirac spectrum
• Decay rates and probability estimates for massive Dirac particles in the Kerr-Newman black hole geometry
• The Casimir effect from the point of view of algebraic quantum field theory
• A new class of fermionic projectors: Møller operators and mass oscillation properties
• Generalized Wentzell boundary conditions and quantum field theory
• An integral spectral representation of the massive Dirac propagator in the Kerr geometry in Eddington-Finkelstein-type coordinates
• The fermionic signature operator in De Sitter spacetime
• Fundamental solutions for the wave operator on static Lorentzian manifolds with timelike boundary
• Algebraic quantum field theory on spacetimes with timelike boundary
• Green-hyperbolic operators on globally hyperbolic spacetimes
• On the Dirichlet problem for \(p\)-harmonic maps. I: Compact targets
• Advances in algebraic quantum field theory
• Smoothness of time functions and the metric splitting of globally hyperbolic spacetimes
• The fermionic signature operator and quantum states in Rindler space-time
• Quantum field theory on curved spacetimes: Axiomatic framework and examples
• Models of Free Quantum Field Theories on Curved Backgrounds
• Sobolev spaces on Riemannian manifolds with bounded geometry: General coordinates and traces
• Introduction to Smooth Manifolds
• Classical and Quantum Fields on Lorentzian Manifolds
• CASIMIR ENERGY FOR A MASSIVE DIRAC FIELD IN ONE SPATIAL DIMENSION: A DIRECT APPROACH
• The fermionic projector in a time-dependent external potential: Mass oscillation property and Hadamard states
• Symmetric positive linear differential equations
• Local boundary conditions for dissipative symmetric linear differential operators
• THE EXTENDED ALGEBRA OF OBSERVABLES FOR DIRAC FIELDS AND THE TRACE ANOMALY OF THEIR STRESS-ENERGY TENSOR
• Dirac Quantum Fields on a Manifold
• Explicit formula and meromorphic extension of the resolvent for the massive Dirac operator in the Schwarzschild-anti-de Sitter spacetime
• On the algebraic quantization of a massive scalar field in anti-de Sitter spacetime
• Differentiability of Solutions to Hyperbolic Initial Boundary Value Problems
• Dirac fields on asymptotically flat space-times
• Boundary Value Problems for Elliptic Differential Operators of First Order
• Domain of Dependence
• Symmetric hyperbolic linear differential equations