FROM EUCLIDEAN FIELD THEORY TO QUANTUM FIELD THEORY

DOI10.1142/S0129055X99000362zbMath0969.81036arXivhep-th/9802035MaRDI QIDQ4519821

Dirk Schlingemann

Publication date: 4 December 2000

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

Full work available at URL: https://arxiv.org/abs/hep-th/9802035

zbMATH Keywords

gauge theoriesWick rotationHaag-Kastler netEuclidean field theoryOsterwalder-Schrader reconstructionWightman theoryWilson loop variablesSchwinger distributions\(C^*\)-algebraic versionEuclidean \(n\)-point functionsinteracting quantum field theory modelstechniques of classical statistical mechanics

Mathematics Subject Classification ID

Axiomatic quantum field theory; operator algebras (81T05) Constructive quantum field theory (81T08) Applications of selfadjoint operator algebras to physics (46L60) Applications of functional analysis in quantum physics (46N50)

Related Items (12)

KMS conditions, standard real subspaces and reflection positivity on the circle group ⋮ Spinors in (anti-)de Sitter space ⋮ Notes on gauge fields and discrete series representations in de Sitter spacetimes ⋮ The Källén-Lehmann representation in de Sitter Spacetime ⋮ Reflection positivity. Abstracts from the workshop held November 26 -- December 2, 2017 ⋮ Operads for algebraic quantum field theory ⋮ Wick rotation for quantum field theories on degenerate Moyal space(-time) ⋮ The algebra of Wick polynomials of a scalar field on a Riemannian manifold ⋮ Infinite volume limits in Euclidean quantum field theory via stereographic projection ⋮ Ricci flow from the renormalization of nonlinear sigma models in the framework of Euclidean algebraic quantum field theory ⋮ Standard subspaces of Hilbert spaces of holomorphic functions on tube domains ⋮ Tensors and spinors in de Sitter space

Cites Work

• On virtual representations of symmetric spaces and their analytic continuation
• Nonexistence of quantum fields associated with two-dimensional spacelike planes
• Construction of \(Y M_ 4\) with an infrared cutoff
• Differential geometry on the space of connections via graphs and projective limits
• Axioms for Euclidean Green's functions
• A<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>λ</mml:mi><mml:mrow><mml:msup><mml:mrow><mml:mi>ϕ</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>Quantum Field Theory without Cutoffs. I

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