Non-commutativity, infinite-dimensionality and probability at the crossroads : proceedings of the RIMS Workshop on Infinite- Dimensional Analysis and Quantum Probability : Kyoto, Japan, 20-22 November, 2001 / editors, Nobuaki Obata, Taku Matsui, Akihito Hora.

Format:

Book

Conference/Event

Contributor:

Obata, Nobuaki, 1957-

Matsui, Taku.

Hora, Akihito.

Conference Name:

RIMS Workshop on Infinite-Dimensional Analysis and Quantum Probability (10th : 2001 : Kyoto, Japan)

Series:

Qp-Pq: Quantum Probability and White Noise Analysis

QP-PQ ; v. 16

Language:

English

Subjects (All):

Dimensional analysis--Congresses.

Dimensional analysis.

Quantum theory--Congresses.

Quantum theory.

Probabilities--Congresses.

Probabilities.

Quantum field theory--Congresses.

Quantum field theory.

Physical Description:

1 online resource (447 p.)

Other Title:

Proceedings of the RIMS Workshop on Infinite-Dimensional Analysis and Quantum Probability

Place of Publication:

Singapore ; River Edge, NJ : World Scientific, c2002.

Language Note:

English

Summary:

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 fourteen research papers deal with most of the current topics, and their interconnections reflect a vivid development in interacting Fock space, infinite-dimensional groups, stochastic independence, non-commutative ce

Contents:

Preface; Contents; Expository Articles; Research Papers; Mathematical Theory of Quantum Particles Interacting with a Quantum Field A . Arai; 1 Introduction; 2 Fock Spaces and Second Quantization; 2.1 Two Kinds of Fock Spaces; 2.2 Second Quantization Operators; 3 Boson Fock Space; 3.1 The Creation and the Annihilation Operators; 3.2 Representation of the CCR; 3.3 Tensor Products of Boson Fock Spaces; 3.4 Basic Estimates; 4 Fermion Fock Space; 5 Description of Models - An Abstract Form; 5.1 Quantum Particle Systems; 5.2 A Composed System of Quantum Particles and a Bose Field

6 A List of Concrete Models6.1 Non-Relativistic QED; 6.2 The Nelson Type Model; 6.3 The Generalized Spin-Boson Model; 6.4 The Dereziriski-Gdrard Model; 6.5 A Particle-Field Model in Relativistic QED; 7 Self-Adjointness of Hamiltonians; '7.1 The Abstract Particle-Field Hamiltonian; 7.2 Hamiltonians in Non-Relativistic QED; A . Existence of Self-Adjoint Extensions; B. Essential Self-Adjointness; 7.3 The GSB and the Dereziriski-Gerard Harniltonians; 7.4 The Dirac-Maxwell Hamiltonian; 8 Existence of Ground States; 8.1 Definition of Ground States and Preliminary Remarks

8.2 An Example-The Abstract van Hove Model8.3 Infrared Singularity; 8.4 Basic Strategies; A . Functional Integral Methods; B. Operator Theoretical Approach; 9 Absence of Ground States; 10 Embedded Eigenvalues, Resonances and Spectral Properties; 11 Scattering Theory; 12 Other Problems; Acknowledgments; References; H-P Quantum Stochastic Differential Equations F. Fagnola; 1 Introduction; 2 Fock Space Notation and Preliminaries; 3 The Left and Right H-P Equations: Preliminaries; 4 The Cocycle Property; 5 The Left H-P Equation with Unbounded G

6 H-P Equations and Dilations of Quantum Markov SemigroupsHypothesis HQDS; 7 The Left H-P Equation with Unbounded GZ: Isometry; 8 The Right H-P Equation with Unbounded F; 9 Dilation of Irreversible Evolutions Arising in Quantum Optics; 10 Dilation of Classical Diffusion Processes; References; Free Relative Entropy and q-Deformation Theory F. Hiai; Introduction; 1 Free Independence; 2 Random Matrices; 3 Free Entropy; 4 Free Relative Entropy for Measures; 4.1 Definition of Free Relative Entropy; 4.2 Free Perturbation Theory for Measures; 4.3 From Relative Entropy to Free Relative Entropy

4.4 Toward the Multivariable Case5 q-Deformation Theory; 5.1 Interpolated Free Group Factors; 5.2 Free Araki- Woods Factors; 5.3 q-Deformed Araki- Woods Algebras; 5.4 The Case q = -1; 5.5 q-Deformed Distributions; References; Quantum White Noise Calculus U. C. Ji & N. Obata; 1 Introduction; 2 Standard CKS-Space; 2.1 Standard Countable Hilbert Space; 2.2 Boson Fock Space and Weighted Fock Space; 2.3 Standard CKS-Space; 2.4 Examples; 2.5 Generating Functions; 3 Characterization Theorems; 3.1 S- Transform and Operator Symbol; 3.2 Unified Characterization Theorem

3.3 Characterization of S-Transform

Notes:

Conference held at the Research Institute for Mathematical Sciences, Kyoto University.

Includes bibliographical references and author index.

ISBN:

9786611908737

9781281908735

1281908738

9789812705242

9812705244