Hilbert modules in quantum electro dynamics and quantum probability

DOI10.1007/s002200050310zbMath0928.46063OpenAlexW2052771093MaRDI QIDQ1268055

Michael Skeide

Publication date: 9 January 2000

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

Full work available at URL: https://doi.org/10.1007/s002200050310

zbMATH Keywords

quantum electrodynamicsHilbert modulesstochastic limitboson field in the vacuum state coupled to a free electroncollective operatorsfree commutation relationsmoments of free creators and annihilatorssymmetric Fock module

Mathematics Subject Classification ID

Electromagnetic interaction; quantum electrodynamics (81V10) Applications of functional analysis in quantum physics (46N50) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) (46H25)

Related Items (22)

A CENTRAL LIMIT THEOREM FOR BOSE ${\mathcal Z}$-INDEPENDENT QUANTUM RANDOM VARIABLES ⋮ Type I product systems of Hilbert modules ⋮ Invariants for \(E_{0}\)-semigroups on II\(_{1}\) factors ⋮ Free white noise flows ⋮ CP-semigroups and dilations, subproduct systems and superproduct systems: the multi-parameter case and beyond ⋮ A new look at Levi-Civita connection in noncommutative geometry ⋮ Classification of 𝐸₀–semigroups by product systems ⋮ Structure of block quantum dynamical semigroups and their product systems ⋮ On the Koszul formula in noncommutative geometry ⋮ Interacting Fock spaces and subproduct systems ⋮ Dilation theory: a guided tour ⋮ Levi-Civita connections for a class of spectral triples ⋮ The Unitarity Conditions for the Square of White Noise ⋮ CONSTRUCTING EXTENSIONS OF CP-MAPS VIA TENSOR DILATIONS WITH THE HELP OF VON NEUMANN MODULES ⋮ UNITS FOR THE TIME-ORDERED FOCK MODULE ⋮ On the index and roots of time ordered product systems ⋮ Quantum stochastic calculus on full Fock modules ⋮ TENSOR PRODUCT SYSTEMS OF HILBERT MODULES AND DILATIONS OF COMPLETELY POSITIVE SEMIGROUPS ⋮ Hilbert von Neumann modules \textit{versus} concrete von Neumann modules ⋮ Couplings to classical and non-classical squeezed white noise as stationary Markov processes ⋮ Algebraic central limit theorems: A personal view on one of Wilhelm’s legacies ⋮ Ideal submodules versus ternary ideals versus linking ideals

This page was built for publication: Hilbert modules in quantum electro dynamics and quantum probability