Choquet-Bruhat Y., DeWitt-Morette C. Analysis, manifolds and physics, vol.2.
PREFACE
This book is a companion volume to our first book, Analysis, Manifolds
and Physics (Revised Edition 1982). In the context of applications of
current interest in physics, we develop concepts and theorems, and
present topics closely related to those of the first book. The first book is
not necessary to the reader interested in Chapters I-V bis and already
familiar with differential geometry nor to the reader interested in Chapter
VI and already familiar with distribution theory. The first book empha-
sizes basics; the second, recent applications.
Applications are the lifeblood of concepts and theorems. They answer
questions and raise questions. We have used them to provide motivation
for concepts and to present new subjects that are still in the developmen-
tal stage. We have presented the applications in the forms of problems
with solutions in order to stress the questions we wish to answer and the
fundamental ideas underlying applications. The reader may also wish to
read only the questions and work out for himself the answers, one of the
best ways to learn how to use a new tool. Occasionally we had to give a
longer-than-usual introduction before presenting the questions. The or-
ganization of questions and answers does not follow a rigid scheme but is
adapted to each problem.
This book is coordinated with the first one as follows:
1. The chapter headings are the same- but in this book, there is no
Chapter VII devoted to infinite dimensional manifolds per se. Instead,
the infinite dimensional applications are treated together with the
corresponding finite imensional ones and can be found throughout
the book.
2. The subheadings of the first book have not been reproduced in the
second one because applications often use properties from several
sections of a chapter. They may even, occasionally, use properties
from subsequent chapters and have been placed according to their
dominant contribution.
3. Page numbers In parentheses refer to the first book. References to
other problems in the present book are indicated [Problem Chapter
Number First Word of Title].
The choice of problems was guided by recent applications of differen-
tial geometry to fundamental problems of physics, as well as by our
personal interests. It is, in part, arbitrary and limited by time, space, and
our desire to bring this project to a close.
The references are not to be construed as an exhaustive bibliography;
they are mainly those that we used while we were preparing a problem or
that we came across shortly after its completion.
The book has been enriched by contributions of Charles Doering,
Harold Grosse, B. Kent Harrison, N.H. Ibragimov, and Carlos Moreno,
and collaborations with Ioannis Bakas, Steven Carlip, Gary Hamrick,
Humberto La Roche and Gary Sammelmann. Discussions with S. Blau,
M. Dubois-Violette, S.G. Low, L.C. Shepley, R. Stora, A.H. Taub, J.
Tits and Jahja Trisnadi are gratefully acknowledged.
The manuscript has been prepared by Ms. Serot Aimeras, Peggy
Caffrey, Jan Duffy and Elizabeth Shepherd.
This work has been supported in part by a grant from the National
Science Foundation PHY 8404931 and a grant INT 8513727 of the
U.S.-France Cooperative Science Program, jointly supported by the NSF
and the Centre National de la Recherche Scientifique.
- pages: 461 pages
- Langue : Anglais
- ISBN: 0444-87071-7
PREFACE
This book is a companion volume to our first book, Analysis, Manifolds
and Physics (Revised Edition 1982). In the context of applications of
current interest in physics, we develop concepts and theorems, and
present topics closely related to those of the first book. The first book is
not necessary to the reader interested in Chapters I-V bis and already
familiar with differential geometry nor to the reader interested in Chapter
VI and already familiar with distribution theory. The first book empha-
sizes basics; the second, recent applications.
Applications are the lifeblood of concepts and theorems. They answer
questions and raise questions. We have used them to provide motivation
for concepts and to present new subjects that are still in the developmen-
tal stage. We have presented the applications in the forms of problems
with solutions in order to stress the questions we wish to answer and the
fundamental ideas underlying applications. The reader may also wish to
read only the questions and work out for himself the answers, one of the
best ways to learn how to use a new tool. Occasionally we had to give a
longer-than-usual introduction before presenting the questions. The or-
ganization of questions and answers does not follow a rigid scheme but is
adapted to each problem.
This book is coordinated with the first one as follows:
1. The chapter headings are the same- but in this book, there is no
Chapter VII devoted to infinite dimensional manifolds per se. Instead,
the infinite dimensional applications are treated together with the
corresponding finite imensional ones and can be found throughout
the book.
2. The subheadings of the first book have not been reproduced in the
second one because applications often use properties from several
sections of a chapter. They may even, occasionally, use properties
from subsequent chapters and have been placed according to their
dominant contribution.
3. Page numbers In parentheses refer to the first book. References to
other problems in the present book are indicated [Problem Chapter
Number First Word of Title].
The choice of problems was guided by recent applications of differen-
tial geometry to fundamental problems of physics, as well as by our
personal interests. It is, in part, arbitrary and limited by time, space, and
our desire to bring this project to a close.
The references are not to be construed as an exhaustive bibliography;
they are mainly those that we used while we were preparing a problem or
that we came across shortly after its completion.
The book has been enriched by contributions of Charles Doering,
Harold Grosse, B. Kent Harrison, N.H. Ibragimov, and Carlos Moreno,
and collaborations with Ioannis Bakas, Steven Carlip, Gary Hamrick,
Humberto La Roche and Gary Sammelmann. Discussions with S. Blau,
M. Dubois-Violette, S.G. Low, L.C. Shepley, R. Stora, A.H. Taub, J.
Tits and Jahja Trisnadi are gratefully acknowledged.
The manuscript has been prepared by Ms. Serot Aimeras, Peggy
Caffrey, Jan Duffy and Elizabeth Shepherd.
This work has been supported in part by a grant from the National
Science Foundation PHY 8404931 and a grant INT 8513727 of the
U.S.-France Cooperative Science Program, jointly supported by the NSF
and the Centre National de la Recherche Scientifique.
