From the Euclidean group to the Poincaré group via Osterwalder-Schrader positivity

DOI10.1007/BF01208260zbMath0522.22016MaRDI QIDQ1055899

Abel Klein, Lawrence J. Landau

Publication date: 1983

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

zbMATH Keywords

unitary representationsanalytic continuationorthogonal projectionsWightman functionsSchwinger functionsEuclidean grouporthochronous Poincare groupOsterwalder-Schrader positivitysymmetric local semigroups

Mathematics Subject Classification ID

Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Applications of Lie groups to the sciences; explicit representations (22E70) Spectral sets of linear operators (47A25)

Related Items (18)

Reflection positivity for the complementary series of SL(2n, \({\mathbb{C}})\) ⋮ Analytic continuation of local representations of symmetric spaces ⋮ KMS conditions, standard real subspaces and reflection positivity on the circle group ⋮ Quantum field theory on curved backgrounds. I: The Euclidean functional integral ⋮ Whittaker modules and quasi-Whittaker modules for the Euclidean Lie algebra \(\mathfrak{e}(3)\) ⋮ Reflection positivity and conformal symmetry ⋮ Reflection positivity. Abstracts from the workshop held November 26 -- December 2, 2017 ⋮ The Berezin form on symmetric $R$-spaces and reflection positivity ⋮ A geometric construction of local representations of local Lie groups ⋮ Wick rotation for quantum field theories on degenerate Moyal space(-time) ⋮ Reflection Positivity for Unitary Representations of Lie Groups ⋮ KMS, ETC. ⋮ Unitary representations of Lie groups with reflection symmetry ⋮ Integrability of unitary representations on reproducing kernel spaces ⋮ Reflection negative kernels and fractional Brownian motion ⋮ Embeddings of the Euclidean algebra $\mathfrak {e}(3)$e(3) into $\mathfrak {sl}(4,\mathbb {C})$sl(4,C) and restrictions of irreducible representations of $\mathfrak {sl}(4,\mathbb {C})$sl(4,C) ⋮ Reflection positive one-parameter groups and dilations ⋮ The 𝒫(𝜑)₂ Model on de Sitter Space

Cites Work

• Unnamed Item
• On virtual representations of symmetric spaces and their analytic continuation
• Construction of a unique self-adjoint generator for a symmetric local semigroup
• Stochastic processes associated with KMS states
• The semigroup characterization of Osterwalder-Schrader path spaces and the construction of Euclidean fields
• Axioms for Euclidean Green's functions
• Clifford modules
• Construction of quantum fields from Markoff fields

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