Quantum Probability for Probabilists
In recent years, the classical theory of stochastic integration and stochastic differential equations has been extended to a non-commutative set-up to develop models for quantum noises. The author, a specialist of classical stochastic calculus and marting
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1538
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Paul-Andre Meyer
Quantum Probability for Probabilists Second Edition
Springer
Author Paul-Andre Meyer Institute de Recherche Mathematique Avancee Universite Louis Pasteur 7, rue Rene Descartes 67048 Strasbourg-Cedex, France
Library of Congress Cataloging-in-Publication Data
Meyer, Paul Andre. Quantum pr o ba b 11 i ty for probab III s t s / Pau I Andre Meyer, -- 2nd ed. p. cm. -- (Lecture notes In mathemat ics ; 1538) Inc I udes bib Ii ograph I ca I references and Index. ISBN 3-540-60270-4 (pbk.) 1. Probabillties. 2. Quantum theory. I. Title. II. Series Lecture notes in mathematiCs (Springer-Verlag) ; 1538. QA3.L28 no. 1538 1995 [OC174.17.P68] 510 s--dc20 [530.1'2'015192] 95-37123 CIP
The present volume is a corrected second edition of the previously published first edition (ISBN 0-540-56476-4). Mathematics Subject Classification (1991): Primary: 81S25 Secondary: 60H05, 60HIO, 60J55, 60J60, 46LXX
ISBN 3-540-60270-4 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1995 Printed in Germany Typesetting: Camera-ready TEX output by the author SPIN: 10479489 46/3142-543210 - Printed on acid-free paper
Introduction
These notes contain all the material accumulated over six years in Strasbourg to teach "Quantum Probability" to myself and to an audience of commutative probabilists. The text, a first version of which appeared in successive volumes of the Seminaire de Probabiliies. has been augmented and carefully rewritten, and translated into international English. Still, it remains true "Lecture Notes" material, and I have resisted suggestions to publish it as a monograph. Being a non-specialist, it is important for me to keep the moderate right to error one has in lectures. The origin of the text also explains the addition "for probabilists" in the title : though much of the material is accessible to the general public, I did not care to redefine Brownian motion or the Ito integral. More precisely than "Quantum Probability", the main topic is "Quantum Stochastic Calculus", a field which has recently got official recognition as 81S25 in the Math. Reviews classification. I find it attractive for two reasons. First, it uses the same language as quantum physics, and does have some relations with it, though possibly not with the kind of fundamental physics mathematicians are fond of. S
