Quantum probability, renormalization and infinite-dimensional *-Lie algebras

DOI10.3842/SIGMA.2009.056zbMath1193.60090arXiv0905.4491OpenAlexW2158109058MaRDI QIDQ970235

Luigi Accardi, Andreas Boukas

Publication date: 17 May 2010

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0905.4491

zbMATH Keywords

renormalizationinfinite dimensional Lie algebrainfinitely divisible processesquantum probabilityquantum white noisecentral extension of Lie algebraMeixmer classesquantum decomposition

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) White noise theory (60H40) String and superstring theories; other extended objects (e.g., branes) in quantum field theory (81T30) Quantum stochastic calculus (81S25) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Stochastic quantization (81S20)

Related Items (8)

A Poisson algebra on the Hida test functions and a quantization using the Cuntz algebra ⋮ \(C^{\ast}\)-non-linear second quantization ⋮ \(q\)-deformation of the square white noise Lie algebra ⋮ Identification of the one-mode quadratic Heisenberg group with the projective group PSU(1,1) and holomorphic representation ⋮ \(C^*\)-quadratic quantization ⋮ The Schrödinger Fock kernel and the no-go theorem for the first order and Renormalized Square of White Noise Lie algebras ⋮ Renormalization and central extensions ⋮ Quadratic exponential vectors

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