free me and my readers from guilt about omitting various important but technical
topics, viewing others from a point of view that physicists may find perverse, failing
to acquire a scholarly knowledge of the literature, and skipping the gruesome details
of certain necessary but boring calculations.
I wish to state emphatically that I am a tourist in the realm of physics myself.
I hope that my foreigner’s perceptions do not do violence to the native culture
and that my lack of expertise has not led to the perpetration of many outright
falsehoods. Given what usually happens when physicists write about mathemat-
ics, however, I dare not hope that there are none. Corrections will be gratefully
received at and recorded on a web page accessible
from (Note added
for the second printing: Numerous small misprints and other errors have been cor-
rected for this printing, and two items have been added to the bibliography. As a
result, the page breaks are different in a few places, and many references have been
renumbered.) The American Mathematical Society will also host a web page for
this book, the URL for which can be found on the back cover above the barcode.
Acknowledgments. I am grateful to the students and colleagues who sat through
the course I offered in 2001 in which I made my rather inept first attempt to
put this material together. Several physicists, particularly David Boulware, have
patiently answered many questions for me, and they are not to blame if their
answers have become distorted in passing through my brain. Finally, an unnamed
referee provided several helpful suggestions and useful references.
The Feynman diagrams in this book were created with JaxoDraw, available at
Gerald B. Folland
Seattle, April 2008
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