White noise analysis and quantum information
"This volume is to pique the interest of many researchers in the fields of infinite dimensional analysis and quantum probability. These fields have undergone increasingly significant developments and have found many new applications, in particular, to classical probability and to different branches of physics. These fields are rather wide and are of a strongly interdisciplinary nature. For such a purpose, we strove to bridge among these interdisciplinary fields in our Workshop on IDAQP and thei…
Read More ↓Title Statements
- Full title :White noise analysis and quantum information / editors, Luigi Accardi [and five others].
Summary
"This volume is to pique the interest of many researchers in the fields of infinite dimensional analysis and quantum probability. These fields have undergone increasingly significant developments and have found many new applications, in particular, to classical probability and to different branches of physics. These fields are rather wide and are of a strongly interdisciplinary nature. For such a purpose, we strove to bridge among these interdisciplinary fields in our Workshop on IDAQP and their Applications that was held at the Institute for Mathematical Sciences, National University of Singapore from 3-7 March 2014. Readers will find that this volume contains all the exciting contributions by well-known researchers in search of new directions in these fields."--Publisher's website
Read More ↓Edition Statements
- Publication Date:2018
Publication Statements
- Publisher(s):World Scientific Publishing Co Pte Ltd
- Place of Publication:Singapore
- Language:eng
- Publication Date:2018
The Physical Object
- Description:1 online resource (xii, 230 pages) : : illustrations
Edition Identifiers
- ISBN:9789813225466, 9813225467, 9789813225473, 9813225475
- oclc:on1007244903
- LC Classification:QA274.29
- Dewey Decimal:519.22
Table of Contents
Foreword; Preface; Extensions of Quantum Theory Canonically Associated to Classical Probability Measures; 1. Introduction; 2. The *-Algebra of Polynomial Functions; 2.1. The polynomial filtration; 2.2. The monomial gradation; 2.3. States on P and probability measures on R; 2.4. Connection with random variables; 2.5. The cyclic representation of (P, ., .); 2.6. Real valued random variables as symmetric operators; 3. The -Orthogonal Polynomials; 3.1. The -orthogonal gradation of P; 3.2. The symmetric Jacobi relation; 3.3. Creation and annihilation operators.
4. The 1-Dimensional Case; 4.1. Monic Jacobi relations; 4.2. Commutation relations in monic form; 4.3. The Gaussian case; 5. Probabilistic Extensions of Quantum Mechanics; 5.1. The generalized free evolution; 5.2. Equilibrium states; References; Hida Distribution Construction of Indefinite Metric (p)d(d 4) Quantum Field Theory; 1. Short Review of a Probabilistic Formulation of Euclidean (4)2; 2. Formulation for d = 4; 3. Well Defined Terms (Feynman Graphs) for d = 4 as Hida Distributions; References; A Mathematical Realization of von Neumann's Measurement Scheme; 1. Introduction.
2. Representation of Measurement Process; 2.1. …
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