Infinite dimensional analysis, quantum probability and applications : QP41 Conference, Al Ain, UAE, March 28-April 1, 2021 / Luigi Accardi, Farrukh Mukhamedov, Ahmed Al Rawashdeh, editors.
International Conference on Infinite Dimensional Analysis, Quantum Probability and Related Topics (41st : 2021 : Online).; Accardi, L. (Luigi), 1947- editor.; Mukhamedov, Farrukh, editor.; Al Rawashdeh, Ahmed, editor.
2022
QC174.85.P76
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Title
Infinite dimensional analysis, quantum probability and applications : QP41 Conference, Al Ain, UAE, March 28-April 1, 2021 / Luigi Accardi, Farrukh Mukhamedov, Ahmed Al Rawashdeh, editors.
Meeting Name
International Conference on Infinite Dimensional Analysis, Quantum Probability and Related Topics (41st : 2021 : Online).
ISBN
9783031061707 (electronic bk.)
3031061705 (electronic bk.)
9783031061691
3031061691
DOI
https://doi.org/10.1007/978-3-031-06170-7
Published
Cham : Springer, [2022]
Copyright
©2022
Language
English
Description
1 online resource (xiii, 378 pages) : illustrations (some color).
Item Number
10.1007/978-3-031-06170-7 doi
Call Number
QC174.85.P76
Dewey Decimal Classification
530.1201/5192
Summary
This proceedings volume gathers selected, peer-reviewed papers presented at the 41st International Conference on Infinite Dimensional Analysis, Quantum Probability and Related Topics (QP41) that was virtually held at the United Arab Emirates University (UAEU) in Al Ain, Abu Dhabi, from March 28th to April 1st, 2021. The works cover recent developments in quantum probability and infinite dimensional analysis, with a special focus on applications to mathematical physics and quantum information theory. Covered topics include white noise theory, quantum field theory, quantum Markov processes, free probability, interacting Fock spaces, and more. By emphasizing the interconnection and interdependence of such research topics and their real-life applications, this reputed conference has set itself as a distinguished forum to communicate and discuss new findings in truly relevant aspects of theoretical and applied mathematics, notably in the field of mathematical physics, as well as an event of choice for the promotion of mathematical applications that address the most relevant problems found in industry. That makes this volume a suitable reading not only for researchers and graduate students with an interest in the field but for practitioners as well.
Note
International conference proceedings.
Includes author index.
Access Note
Access limited to authorized users.
Added Author
Accardi, L. (Luigi), 1947- editor.
Mukhamedov, Farrukh, editor.
Al Rawashdeh, Ahmed, editor.
Series
Springer proceedings in mathematics & statistics ; v.390.
Available in Other Form
Infinite dimensional analysis, quantum probability and applications.
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Intro
Organization
Preface
Contents
Part I Quantum Probability Methods
The Non-linear and Quadratic Quantization Programs
1 Introduction
1.1 Quadratic Quantization
2 Some Properties of *-Lie Algebras
2.1 The Complex d-Dimensional Heisenberg Algebra: heis1,d(0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900)
2.2 The Complex d-Dimensional Quadratic Heisenberg Algebra heis2,d(0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900)
3 The Symplectic Approach to Homogeneous Quadratic Boson Fields

3.1 The *-Lie Algebra of Homogeneous Quadratic Boson Fields
3.2 Identification of the *-Lie Algebra of Homogeneous Quadratic Boson Fields with heis2,d(0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900)
3.3 Central Decomposition of heis2,d(0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900): heis2,d,cls(0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900)
4 The Complex Symplectic *-Lie Algebra sp(2d, 0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900)

4.1 The Involution on sp(2d, 0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900) : sp(2d, 0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900)
4.2 *-Isomorphism Between heis2,d, cls(0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900) and sp(2d,0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900)
4.3 The Isomorphism Between heis2,d(0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900) and sp(2d, 0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900) : Direct Proof

5 Real Lie Sub-algebras of heis2,d(0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900) and spskew,(2d,0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900)
5.1 Real *-Lie Algebra-Isomorphism Between spskew,(2d,0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900) and sp-(2d,IR)
6 Vacuum Averages
7 Lie Groups Associated with the Symplectic Algebra
7.1 The Siegel Unit Disk
7.2 The Metaplectic Group
7.3 The Abstract Symplectic Algebra and Its Lie Groups
8 The Problems of Diagonalizability and Vacuum Factorizability

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