Hadamard states for quantized Dirac fields on Lorentzian manifolds of bounded geometry

Abstract

We consider Dirac equations on even dimensional Lorentzian manifolds of bounded geometry with a spin structure. For the associated free quantum field theory, we construct pure Hadamard states using global pseudodifferential calculus on a Cauchy surface. We also give two constructions of Hadamard states for Dirac fields for arbitrary spacetimes with a spin structure.(2nd revised version). Will appear in Rev. Math. Phys.

References in corpus (19)

• On smooth Cauchy hypersurfaces and Geroch's splitting theorem
• Smoothness of time functions and the metric splitting of globally hyperbolic spacetimes
• Generalized Cylinders in Semi-Riemannian and Spin Geometry
• Microlocal spectrum condition and Hadamard form for vector-valued quantum fields in curved spacetime
• Passivity and microlocal spectrum condition
• The Hadamard Condition for Dirac Fields and Adiabatic States on Robertson-Walker Spacetimes
• Construction of Hadamard states by pseudo-differential calculus
• Hadamard states for the Klein-Gordon equation on Lorentzian manifolds of bounded geometry
• The locally covariant Dirac field
• Nuclearity, Local Quasiequivalence and Split Property for Dirac Quantum Fields in Curved Spacetime
• A Non-Perturbative Construction of the Fermionic Projector on Globally Hyperbolic Manifolds I - Space-Times of Finite Lifetime
• A Non-Perturbative Construction of the Fermionic Projector on Globally Hyperbolic Manifolds II -- Space-Times of Infinite Lifetime
• Hadamard property of the in and out states for Klein-Gordon fields on asymptotically static spacetimes
• The stress energy tensor of a locally supersymmetric quantum field on a curved spacetime
• Singularity structure of the two point function of the free Dirac field on a globally hyperbolic spacetime
• Cauchy Problem and Green's Functions for First Order Differential Operators and Algebraic Quantization
• Persistence of noncompact normally hyperbolic invariant manifolds in bounded geometry
• Intertwining operators for symmetric hyperbolic systems on globally hyperbolic manifolds
• $L^p$-spectrum of the Dirac operator on products with hyperbolic spaces

Cited by in corpus (4)

• Quantum Field Theory in Curved Spacetime (2nd Edition)
• An index theorem on asymptotically static spacetimes with compact Cauchy surface
• The Quantization of Maxwell Theory in the Cauchy Radiation Gauge: Hodge Decomposition and Hadamard States
• Hadamard property of the in and out states for Dirac fields on asymptotically static spacetimes