Reflection positivity and monotonicity

DOI10.1063/1.2907660zbMath1152.81489arXiv0705.0712OpenAlexW3103526144WikidataQ124969575 ScholiaQ124969575MaRDI QIDQ5504901

Arthur Jaffe, William Gordon Ritter

Publication date: 23 January 2009

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

Full work available at URL: https://arxiv.org/abs/0705.0712

zbMATH Keywords

Riemannian manifoldinequalityreflection positivityscalar fieldsDirac fieldsDirichlet covariance operatorNeumann covariance operator

Mathematics Subject Classification ID

Quantum field theory on curved space or space-time backgrounds (81T20) Elliptic equations on manifolds, general theory (58J05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Constructive quantum field theory (81T08) Applications of PDEs on manifolds (58J90) Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70)

Related Items (14)

Derivations and reflection positivity on the quantum cylinder ⋮ Symmetric spaces with dissecting involutions ⋮ Reflection positivity in higher derivative scalar theories ⋮ Reflection positivity and conformal symmetry ⋮ Infinite volume limits in Euclidean quantum field theory via stereographic projection ⋮ Quantum fields from global propagators on asymptotically Minkowski and extended de Sitter spacetimes ⋮ Reflection positivity on spheres ⋮ A universal envelope for Gaussian processes and their kernels ⋮ Reflection positivity, duality, and spectral theory ⋮ A construction of Euclidean invariant, reflection positive measures on a compactification of distributions ⋮ Nonexistence of Skyrmion–Skyrmion and Skyrmion–anti-Skyrmion static equilibria ⋮ Reflection positive one-parameter groups and dilations ⋮ The 𝒫(𝜑)₂ Model on de Sitter Space ⋮ Instability of enclosed horizons

Cites Work

• Reflection groups on Riemannian manifolds
• Quantum field theory on curved backgrounds. I: The Euclidean functional integral
• Analysis of the Laplacian on a complete Riemannian manifold
• Random fields on Riemannian manifolds: A constructive approach
• A note on reflection positivity
• Unbounded, symmetric semigroups on a separable Hilbert space are essentially selfadjoint
• Construction of a unique self-adjoint generator for a symmetric local semigroup
• Axioms for Euclidean Green's functions. II
• Equivariant maps and purely atomic spectrum
• Axioms for Euclidean Green's functions
• Schrödinger operators with singular potentials
• Construction of quantum fields from Markoff fields
• Essential self-adjointness of powers of generators of hyperbolic equations
• MARKOV QUANTUM FIELDS ON A MANIFOLD
• The Harmonic Operator for Exterior Differential Forms

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