Transforms in Quantum White Noise

Transforms in Quantum White Noise

Author: Un Cig Ji

Publisher: World Scientific Publishing Company

ISBN: 9814635545

Category: Mathematics

Page: 250

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This book is the first comprehensive monograph focusing on the recent developments of quantum white noise calculus and its applications. Quantum white noise calculus is a quantum extension of the Gaussian white noise calculus and provides a useful toolbox for the analysis of operators on Boson Fock space based on an infinite dimensional distribution theory of Schwartz type. This volume starts with the famous Wiener-Ito-Segal isomorphism between the Fock space and the L2-space over a Gaussian space, and systematically constructs Gelfand triples along which white noise operators are defined. The white noise operators cover a wide class of operators on Fock space including pointwisely defined annihilation and creation operators called quantum white noise and a white noise operator is regarded as a function of quantum white noise. The main purpose of this volume is to describe the new concept of quantum white noise derivatives, a kind of functional derivative for white noise operators. This idea leads to a new type of differential equations for white noise operators with applications in stochastic analysis and quantum physics. In particular, transforms of white noise functions and operators such as Fourier-Gauss transform, Fourier-Mehler transform, Bogoliubov transform, and quantum Girsanov transform are characterized as solutions to differential equations of new type. The development of quantum white noise derivative sheds fresh light on the study of Fock space operators.
Transforms in Quantum White Noise
Language: un
Pages: 250
Authors: Un Cig Ji, Nobuaki Obata
Categories: Mathematics
Type: BOOK - Published: 2020-04-29 - Publisher: World Scientific Publishing Company

This book is the first comprehensive monograph focusing on the recent developments of quantum white noise calculus and its applications. Quantum white noise calculus is a quantum extension of the Gaussian white noise calculus and provides a useful toolbox for the analysis of operators on Boson Fock space based on
Quantum Probability and Infinite Dimensional Analysis
Language: en
Pages: 304
Authors: Habib Ouerdiane, Abdessatar Barhoumi
Categories: Mathematics
Type: BOOK - Published: 2010 - Publisher: World Scientific

This is the proceedings of the 29th Conference on Quantum Probability and Infinite Dimensional Analysis, which was held in Hammamet, Tunisia.
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Pages: 208
Authors: Hida Takeyuki, Saito Kimiaki
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Non-commutativity, Infinite-dimensionality and Probability at the Crossroads
Language: en
Pages: 437
Authors: Nobuaki Obata
Categories: Dimensional analysis
Type: BOOK - Published: 2003-01-16 - Publisher: World Scientific

Infinite-dimensional analysis and quantum probability have undergone significant developments in the last few years and created many applications. This volume includes four expository articles on recent developments in quantum field theory, quantum stochastic differential equations, free probability and quantum white noise calculus, which are targeted also for graduate study. The
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Language: un
Pages: 245
Authors: Hui-Hsiung Kuo, Ambar N. Sengupta, Padmanabhan Sundar
Categories: Mathematics
Type: BOOK - Published: 2008 - Publisher: World Scientific

This volume contains current work at the frontiers of research in infinite dimensional stochastic analysis. It presents a carefully chosen collection of articles by experts to highlight the latest developments in white noise theory, infinite dimensional transforms, quantum probability, stochastic partial differential equations, and applications to mathematical finance. Included in