Microlocal analysis of quantum fields on curved spacetimes: Analytic wavefront sets and Reeh-Schlieder theorems

Abstract

We show in this article that the Reeh-Schlieder property holds for states of quantum fields on real analytic spacetimes if they satisfy an analytic microlocal spectrum condition. This result holds in the setting of general quantum field theory, i.e. without assuming the quantum field to obey a specific equation of motion. Moreover, quasifree states of the Klein-Gordon field are further investigated in this work and the (analytic) microlocal spectrum condition is shown to be equivalent to simpler conditions. We also prove that any quasifree ground- or KMS-state of the Klein-Gordon field on a stationary real analytic spacetime fulfills the analytic microlocal spectrum condition.

31 pages, latex2e

References in corpus (5)

• Local Wick Polynomials and Time Ordered Products of Quantum Fields in Curved Spacetime
• Existence of Local Covariant Time Ordered Products of Quantum Fields in Curved Spacetime
• Causal and localizable quantum operations
• Adiabatic vacuum states on general spacetime manifolds: Definition, construction, and physical properties
• The asymptotic symmetry of de Sitter spacetime

Cited by in corpus (48)

• Notes on Some Entanglement Properties of Quantum Field Theory
• Boundary-to-bulk maps for AdS causal wedges and the Reeh-Schlieder property in holography
• Algebraic QFT in Curved Spacetime and quasifree Hadamard states: an introduction
• The Necessity of the Hadamard Condition
• The extended algebra of observables for Dirac fields and the trace anomaly of their stress-energy tensor
• Quantum out-states holographically induced by asymptotic flatness: Invariance under spacetime symmetries, energy positivity and Hadamard property
• Equivalence of the (generalised) Hadamard and microlocal spectrum condition for (generalised) free fields in curved spacetime
• On the initial conditions and solutions of the semiclassical Einstein equations in a cosmological scenario
• The IR stability of de Sitter QFT: Physical initial conditions
• Construction of Hadamard states by pseudo-differential calculus
• Distillability and positivity of partial transposes in general quantum field systems
• The locally covariant Dirac field
• Distinguished quantum states in a class of cosmological spacetimes and their Hadamard property
• Quantum imprints of gravitational shockwaves
• On the Reeh-Schlieder Property in Curved Spacetime
• Macroscopic aspects of the Unruh effect
• On the construction of Hartle-Hawking-Israel states across a static bifurcate Killing horizon
• Thermal equilibrium states of a linear scalar quantum field in stationary spacetimes
• Weakly coupled local particle detectors cannot harvest entanglement
• Locally covariant quantum field theory and the problem of formulating the same physics in all spacetimes
• Generally covariant dynamical reduction models and the Hadamard condition
• Generalized Wentzell boundary conditions and quantum field theory
• Gupta-Bleuler Quantization of the Maxwell Field in Globally Hyperbolic Space-Times
• An intuitive construction of modular flow
• General features of the thermalization of particle detectors and the Unruh effect
• The art of the state
• A Gutzwiller trace formula for stationary space-times
• Construction of the Unruh State for a Real Scalar Field on the Kerr-de Sitter Spacetime
• Quantum Field Theory in Curved Spacetime (2nd Edition)
• Pure quasifree states of the Dirac field from the fermionic projector
• Snowmass White Paper: The Quest to Define QFT
• Quantum field theory in static external potentials and Hadamard states
• Essential self-adjointness of Wick squares in quasi-free Hadamard representations on curved spacetimes
• A mathematical analysis of Casimir interactions I: The scalar field
• A mechanism for holography for non-interacting fields on anti-de Sitter spacetimes
• Wick rotation of the time variables for two-point functions on analytic backgrounds
• The classical and quantum photon field for non-compact manifolds with boundary and in possibly inhomogeneous media
• Quantum physics, fields and closed timelike curves: The D-CTC condition in quantum field theory
• Local vs. global temperature under a positive curvature condition
• The Cosmological Semiclassical Einstein Equation as an Infinite-Dimensional Dynamical System
• Local incompatibility of the microlocal spectrum condition with the KMS property along spacelike directions in quantum field theory on curved spacetime
• Local Thermal Equilibrium States in Relativistic Quantum Field Theory
• Relational bulk reconstruction from modular flow
• Hadamard property of the Unruh state for massless fermions on Kerr spacetime : the large $a$ case
• Hadamard states for bosonic quantum field theory on globally hyperbolic spacetimes
• The microlocal irregularity of Gaussian noise
• Quantum fields on semi-globally hyperbolic space-times
• A Quantum Energy Inequality for a Non-commutative QFT