The Wigner semi-circle law in quantum electro dynamics

DOI10.1007/BF02099625zbMath0856.46047MaRDI QIDQ1924102

Luigi Accardi, Yun Gang Lu

Publication date: 24 February 1997

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

zbMATH Keywords

quantum noisestochastic limit of quantum theoryinteracting Fock spacequantum electromagnetic fieldquantum electro-dynamicsnonlinear generalization of the Fermi golden rulequantum stochastic calculus on a Hilbert module

Mathematics Subject Classification ID

Electromagnetic interaction; quantum electrodynamics (81V10) Quantum stochastic calculus (81S25) Applications of functional analysis in quantum physics (46N50) Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) (46H25)

Related Items (28)

ROTATION INVARIANT INTERACTING FOCK SPACES ⋮ The quantum moment problem for a classical random variable and a classification of interacting Fock spaces ⋮ On the multi-dimensional Favard lemma ⋮ Central limit theorems for large graphs: Method of quantum decomposition ⋮ Module white noise calculus ⋮ The generalized Fibonacci oscillator as an open quantum system ⋮ Free white noise flows ⋮ Quantum stochastic integral representations on interacting Fock space ⋮ The Quantum Mechanics Canonically Associated to Free Probability II: The Normal and Inverse Normal Order Problem ⋮ Detailed balance as a quantum-group symmetry of Kraus operators ⋮ Non-exponential decay for polaron model ⋮ Free probability and quantum electrodynamics ⋮ Interacting Fock spaces and subproduct systems ⋮ Dynamics of an atom cavity field system in interacting Fock space ⋮ CHARACTERIZATION OF PROBABILITY MEASURES THROUGH THE CANONICALLY ASSOCIATED INTERACTING FOCK SPACES ⋮ Nuclear Realization of Virasoro–Zamolodchikov-w_∞⋆-Lie Algebras Through the Renormalized Higher Powers of Quantum Meixner White Noise ⋮ SCALING LIMIT FOR GIBBS STATES OF JOHNSON GRAPHS AND RESULTING MEIXNER CLASSES ⋮ WHITE NOISE LÉVY–MEIXNER PROCESSES THROUGH A TRANSFER PRINCIPAL FROM ONE-MODE TO ONE-MODE TYPE INTERACTING FOCK SPACES ⋮ The qq-bit (III): Symmetric q-Jordan–Wigner embeddings ⋮ ANALYTIC CHARACTERIZATION OF ONE-MODE INTERACTING FOCK SPACE ⋮ A new algebra in the stochastic approximation for the model of a particle interacting with a quantum field ⋮ Interacting Fock Spaces Related to the Anderson Model ⋮ The qq-bit (I): Central limits with left q-Jordan–Wigner embeddings, monotone interacting Fock space, Azema random variable, probabilistic meaning of q ⋮ Interacting Fock Spaces and Gaussianization of Probability Measures ⋮ The Free Stochastic Limit of Interacting Quantum Fields ⋮ The Semi-Circle Diagrams in the Stochastic Limit of the Anderson Model ⋮ 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

Cites Work

• A new example of `independence' and `white noise'
• Stochastic integration on the Cuntz algebra \({\mathcal O}_ \infty\)
• Induced representations of C\(^*\)-algebras
• Random Matrices in Physics
• Inner Product Modules Over B ∗ -Algebras
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