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Academic Press, 1979. 308 pages.

In the summer of 1977 I was invited to lecture in the Troisieme Cycle de la

Suisse Romande, a consortium of four universities in the French-speaking

part of Switzerland. There was some discussion of the topic about which I

might speak. Since I seem fated to be the apostle of probability to Swiss

physics (see [258]), we agreed on the general topic of "path integral

techniques." I decided to limit myself to the well-defined Wiener integral

rather than the often ill-defined Feynman integral. In preparing my lectures

I was struck by the mathematical beauty of the material, especially some

of the ideas about which I had previously been unfamiliar. I was also

struck by the dearth of "expository" literature on the connection between

Wiener integral techniques and their application to rather detailed ques-

tions in differential equations, especially those of quantum physics; it

seemed that path integrals were an extremely powerful tool used as a kind

of secret weapon by a small group of mathematical physicists. My pur-

pose here is to rectify this situation. I hope not only to have made

available new tools to practicing mathematical physicists but also to have

opened up new areas of research to probabilists.

I am pleased to be able to thank some of my colleagues who aided me in

the preparation of this book. During the period of the lectures on which

the book is based, I was a guest of the Physics Department of the

University of Geneva. I am grateful to M. Guenin, the departmental

chairman, and most especially to J. P. Eckmann for making my visit

possible. The lectures were given at the EPFL in Lausanne; P. Choquard

was a most gracious host there. I should like to thank the Secretariat

Centrale of the University of Geneva Physics Department and Mrs. G.

Anderson of the Princeton Physics Department for typing the first and

second drafts, respectively, of the manuscript. I am also grateful to Y.

Kannai for the hospitality of the Weizmann Institute Pure Mathematics

Department where Sections 20-24 were written.

Finally, I owe a debt to a number of people for scientific contributions:

M. Donsker and M. Kac made various valuable suggestions about what

topics might be included as well as offering help on technical questions; L.

van Hemmen gave his permission to use an unpublished argument of his; I

had valuable discussions with M. Aizenman, R. Carmona, P. Deift, J. P.

Eckmann, J. Frohlich, C. Gruber, E. Lieb, A. Sokal, M. Taylor, A.

Truman, and S. R. S. Varadhan; the careful reading of the complete manu-

script by R. Carmona was especially valuable; finally, M. Klaus, A.

Kupiainen, and K. Miller helped in the proofreading. I am glad to be able

to thank all these individuals for their help.

In the summer of 1977 I was invited to lecture in the Troisieme Cycle de la

Suisse Romande, a consortium of four universities in the French-speaking

part of Switzerland. There was some discussion of the topic about which I

might speak. Since I seem fated to be the apostle of probability to Swiss

physics (see [258]), we agreed on the general topic of "path integral

techniques." I decided to limit myself to the well-defined Wiener integral

rather than the often ill-defined Feynman integral. In preparing my lectures

I was struck by the mathematical beauty of the material, especially some

of the ideas about which I had previously been unfamiliar. I was also

struck by the dearth of "expository" literature on the connection between

Wiener integral techniques and their application to rather detailed ques-

tions in differential equations, especially those of quantum physics; it

seemed that path integrals were an extremely powerful tool used as a kind

of secret weapon by a small group of mathematical physicists. My pur-

pose here is to rectify this situation. I hope not only to have made

available new tools to practicing mathematical physicists but also to have

opened up new areas of research to probabilists.

I am pleased to be able to thank some of my colleagues who aided me in

the preparation of this book. During the period of the lectures on which

the book is based, I was a guest of the Physics Department of the

University of Geneva. I am grateful to M. Guenin, the departmental

chairman, and most especially to J. P. Eckmann for making my visit

possible. The lectures were given at the EPFL in Lausanne; P. Choquard

was a most gracious host there. I should like to thank the Secretariat

Centrale of the University of Geneva Physics Department and Mrs. G.

Anderson of the Princeton Physics Department for typing the first and

second drafts, respectively, of the manuscript. I am also grateful to Y.

Kannai for the hospitality of the Weizmann Institute Pure Mathematics

Department where Sections 20-24 were written.

Finally, I owe a debt to a number of people for scientific contributions:

M. Donsker and M. Kac made various valuable suggestions about what

topics might be included as well as offering help on technical questions; L.

van Hemmen gave his permission to use an unpublished argument of his; I

had valuable discussions with M. Aizenman, R. Carmona, P. Deift, J. P.

Eckmann, J. Frohlich, C. Gruber, E. Lieb, A. Sokal, M. Taylor, A.

Truman, and S. R. S. Varadhan; the careful reading of the complete manu-

script by R. Carmona was especially valuable; finally, M. Klaus, A.

Kupiainen, and K. Miller helped in the proofreading. I am glad to be able

to thank all these individuals for their help.

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