Quantum Stochastic Calculus And Representations Of Lie Superalgebras

Author : Timothy M.W. Eyre
Publisher : Springer
Page : 142 pages
File Size : 47,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540683858

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Quantum Stochastic Calculus and Representations of Lie Superalgebras by Timothy M.W. Eyre Pdf

This book describes the representations of Lie superalgebras that are yielded by a graded version of Hudson-Parthasarathy quantum stochastic calculus. Quantum stochastic calculus and grading theory are given concise introductions, extending readership to mathematicians and physicists with a basic knowledge of algebra and infinite-dimensional Hilbert spaces. The develpment of an explicit formula for the chaotic expansion of a polynomial of quantum stochastic integrals is particularly interesting. The book aims to provide a self-contained exposition of what is known about Z_2-graded quantum stochastic calculus and to provide a framework for future research into this new and fertile area.

Author : Timothy M. W. Eyre
Publisher : Unknown
Page : 138 pages
File Size : 52,5 Mb
Release : 1998
Category : Electronic
ISBN : OCLC:1132032607

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Quantum Stochastic Calculus and Representations for Lie Superalgebras by Timothy M. W. Eyre Pdf

Author : U. Franz,René Schott
Publisher : Springer Science & Business Media
Page : 233 pages
File Size : 50,8 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9789401592772

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Stochastic Processes and Operator Calculus on Quantum Groups by U. Franz,René Schott Pdf

This book aims to present several new developments on stochastic processes and operator calculus on quantum groups. Topics which are treated include operator calculus, dual representations, stochastic processes and diffusions, Appell polynomials and systems in connection with evolution equations. Audience: This volume contains introductory material for graduate students who are new to the field, as well as more advanced material for specialists in probability theory, algebraic structures, representation theory, mathematical physics and theoretical physics.

Author : Uwe Franz,Nicolas Privault
Publisher : Cambridge University Press
Page : 303 pages
File Size : 49,8 Mb
Release : 2016-01-25
Category : Mathematics
ISBN : 9781107128651

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Probability on Real Lie Algebras by Uwe Franz,Nicolas Privault Pdf

This monograph is a progressive introduction to non-commutativity in probability theory, summarizing and synthesizing recent results about classical and quantum stochastic processes on Lie algebras. In the early chapters, focus is placed on concrete examples of the links between algebraic relations and the moments of probability distributions. The subsequent chapters are more advanced and deal with Wigner densities for non-commutative couples of random variables, non-commutative stochastic processes with independent increments (quantum Lévy processes), and the quantum Malliavin calculus. This book will appeal to advanced undergraduate and graduate students interested in the relations between algebra, probability, and quantum theory. It also addresses a more advanced audience by covering other topics related to non-commutativity in stochastic calculus, Lévy processes, and the Malliavin calculus.

Author : Alain Connes,Joachim Cuntz,Erik G. Guentner,Nigel Higson,Jerome Kaminker,John E. Roberts
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 43,5 Mb
Release : 2003-12-08
Category : Mathematics
ISBN : 3540203575

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Noncommutative Geometry by Alain Connes,Joachim Cuntz,Erik G. Guentner,Nigel Higson,Jerome Kaminker,John E. Roberts Pdf

Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.

Author : S Attal,J M Lindsay
Publisher : World Scientific
Page : 604 pages
File Size : 53,8 Mb
Release : 2003-06-27
Category : Science
ISBN : 9789814485593

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Quantum Probability Communications by S Attal,J M Lindsay Pdf

0Keywords:Mathematics;Mathematical Physics;Quantum Probability;Stochastic Calculus;Noncommutative Probability;Free Probability

Author : J. M Lindsay
Publisher : World Scientific
Page : 294 pages
File Size : 48,9 Mb
Release : 2003
Category : Science
ISBN : 9789812389596

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Quantum Probability Communications Qp-Pq by J. M Lindsay Pdf

Lecture notes from a Summer School on Quantum Probability held at the University of Grenoble are collected in these two volumes of the QP-PQ series. The articles have been refereed and extensively revised for publication. It is hoped that both current and future students of quantum probability will be engaged, informed and inspired by the contents of these two volumes. An extensive bibliography containing the references from all the lectures is included in Volume 12.

Author : Jim Pitman
Publisher : Springer
Page : 260 pages
File Size : 54,6 Mb
Release : 2006-07-21
Category : Mathematics
ISBN : 9783540342663

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Combinatorial Stochastic Processes by Jim Pitman Pdf

The purpose of this text is to bring graduate students specializing in probability theory to current research topics at the interface of combinatorics and stochastic processes. There is particular focus on the theory of random combinatorial structures such as partitions, permutations, trees, forests, and mappings, and connections between the asymptotic theory of enumeration of such structures and the theory of stochastic processes like Brownian motion and Poisson processes.

Author : Palle Jorgensen,James Tian
Publisher : World Scientific
Page : 253 pages
File Size : 44,5 Mb
Release : 2021-01-15
Category : Mathematics
ISBN : 9789811225796

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Infinite-dimensional Analysis: Operators In Hilbert Space; Stochastic Calculus Via Representations, And Duality Theory by Palle Jorgensen,James Tian Pdf

The purpose of this book is to make available to beginning graduate students, and to others, some core areas of analysis which serve as prerequisites for new developments in pure and applied areas. We begin with a presentation (Chapters 1 and 2) of a selection of topics from the theory of operators in Hilbert space, algebras of operators, and their corresponding spectral theory. This is a systematic presentation of interrelated topics from infinite-dimensional and non-commutative analysis; again, with view to applications. Chapter 3 covers a study of representations of the canonical commutation relations (CCRs); with emphasis on the requirements of infinite-dimensional calculus of variations, often referred to as Ito and Malliavin calculus, Chapters 4-6. This further connects to key areas in quantum physics.

Author : David Applebaum,B.V. Rajarama Bhat,Johan Kustermans,J. Martin Lindsay
Publisher : Springer
Page : 299 pages
File Size : 42,8 Mb
Release : 2005-09-14
Category : Mathematics
ISBN : 9783540314509

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Quantum Independent Increment Processes I by David Applebaum,B.V. Rajarama Bhat,Johan Kustermans,J. Martin Lindsay Pdf

This volume is the first of two volumes containing the revised and completed notes lectures given at the school "Quantum Independent Increment Processes: Structure and Applications to Physics". This school was held at the Alfried-Krupp-Wissenschaftskolleg in Greifswald during the period March 9 – 22, 2003, and supported by the Volkswagen Foundation. The school gave an introduction to current research on quantum independent increment processes aimed at graduate students and non-specialists working in classical and quantum probability, operator algebras, and mathematical physics. The present first volume contains the following lectures: "Lévy Processes in Euclidean Spaces and Groups" by David Applebaum, "Locally Compact Quantum Groups" by Johan Kustermans, "Quantum Stochastic Analysis" by J. Martin Lindsay, and "Dilations, Cocycles and Product Systems" by B.V. Rajarama Bhat.

Author : Vassili N. Kolokoltsov
Publisher : Springer
Page : 360 pages
File Size : 47,6 Mb
Release : 2007-12-03
Category : Mathematics
ISBN : 9783540465874

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Semiclassical Analysis for Diffusions and Stochastic Processes by Vassili N. Kolokoltsov Pdf

The monograph is devoted mainly to the analytical study of the differential, pseudo-differential and stochastic evolution equations describing the transition probabilities of various Markov processes. These include (i) diffusions (in particular,degenerate diffusions), (ii) more general jump-diffusions, especially stable jump-diffusions driven by stable Lévy processes, (iii) complex stochastic Schrödinger equations which correspond to models of quantum open systems. The main results of the book concern the existence, two-sided estimates, path integral representation, and small time and semiclassical asymptotics for the Green functions (or fundamental solutions) of these equations, which represent the transition probability densities of the corresponding random process. The boundary value problem for Hamiltonian systems and some spectral asymptotics ar also discussed. Readers should have an elementary knowledge of probability, complex and functional analysis, and calculus.

Author : K.R. Parthasarathy
Publisher : Birkhäuser
Page : 299 pages
File Size : 54,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034886413

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An Introduction to Quantum Stochastic Calculus by K.R. Parthasarathy Pdf

"Elegantly written, with obvious appreciation for fine points of higher mathematics...most notable is [the] author's effort to weave classical probability theory into [a] quantum framework." – The American Mathematical Monthly "This is an excellent volume which will be a valuable companion both for those who are already active in the field and those who are new to it. Furthermore there are a large number of stimulating exercises scattered through the text which will be invaluable to students." – Mathematical Reviews An Introduction to Quantum Stochastic Calculus aims to deepen our understanding of the dynamics of systems subject to the laws of chance both from the classical and the quantum points of view and stimulate further research in their unification. This is probably the first systematic attempt to weave classical probability theory into the quantum framework and provides a wealth of interesting features: The origin of Ito's correction formulae for Brownian motion and the Poisson process can be traced to communication relations or, equivalently, the uncertainty principle. Quantum stochastic interpretation enables the possibility of seeing new relationships between fermion and boson fields. Quantum dynamical semigroups as well as classical Markov semigroups are realized through unitary operator evolutions. The text is almost self-contained and requires only an elementary knowledge of operator theory and probability theory at the graduate level.

Author : L. Accardi,C.C. Heyde
Publisher : Springer Science & Business Media
Page : 370 pages
File Size : 53,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461222248

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Probability Towards 2000 by L. Accardi,C.C. Heyde Pdf

Senior probabilists from around the world with widely differing specialities gave their visions of the state of their specialty, why they think it is important, and how they think it will develop in the new millenium. The volume includes papers given at a symposium at Columbia University in 1995, but papers from others not at the meeting were added to broaden the coverage of areas. All papers were refereed.

Author : Ole E. Barndorff-Nielsen
Publisher : Springer Science & Business Media
Page : 364 pages
File Size : 51,5 Mb
Release : 2006
Category : Distribution
ISBN : 3540244077

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Quantum Independent Increment Processes II by Ole E. Barndorff-Nielsen Pdf

Lectures given at the school "Quantum Independent Increment Processes: Structure and Applications to Physics" held at the Alfried-Krupp-Wissenschaftskolleg in Greifswald in March 9-22, 2003.

Author : Stéphane Attal,Alain Joye,claude-alain pillet
Publisher : Springer
Page : 329 pages
File Size : 51,5 Mb
Release : 2006-08-18
Category : Mathematics
ISBN : 9783540339229

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Open Quantum Systems I by Stéphane Attal,Alain Joye,claude-alain pillet Pdf

Understanding dissipative dynamics of open quantum systems remains a challenge in mathematical physics. This problem is relevant in various areas of fundamental and applied physics. Significant progress in the understanding of such systems has been made recently. These books present the mathematical theories involved in the modeling of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications.