Quadratic representations of the canonical commutation relations

DOI10.2977/prims/1195163718zbMath0845.46045OpenAlexW2006560696MaRDI QIDQ1913418

George Reents, Martin Proksch, Stephen Jeffrey Summers

Publication date: 8 July 1996

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1195163718

zbMATH Keywords

quantum field theoryWeyl algebraFock representationquantum opticsquadratic representationscanonical commutation relations over symplectic spaces of arbitrary dimensioncanonical quadratic transformationscoherent and symplectic quasifree representations

Mathematics Subject Classification ID

Applications of functional analysis in quantum physics (46N50) Commutation relations and statistics as related to quantum mechanics (general) (81S05)

Related Items

L²(E*, μ)-WEYL REPRESENTATIONS, Polynomial Weyl representations

Cites Work

• The smallest C\(^*\)-algebra for canonical commutation relations
• The \(C^ *\)-algebras of a free Boson field
• Quasi-free states of the C.C.R.-algebra and Bogoliubov transformations
• A Gårding domain for quantum fields
• On factor representations and the \(C^ *\)-algebra of canonical commutation relations
• Tensor Algebras Over Hilbert Spaces. I
• Nonlinear canonical transformations. I
• Generators for nonlinear canonical transformations
• Linear Symmetries of Free Boson Fields
• Gårding Domains and Analytic Vectors for Quantum Fields
• The Mathematics of Second Quantization
• REPRESENTATIONS OF THE COMMUTATION RELATIONS
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