SURV/149

Quantum field theory has been a great success for physics, but it

is difficult for mathematicians to learn because it is mathemati-

cally incomplete. Folland, who is a mathematician, has spent

considerable time digesting the physical theory and sorting out the

mathematical issues in it. Fortunately for mathematicians, Folland

is a gifted expositor.

The purpose of this book is to present the elements of quantum

field theory, with the goal of understanding the behavior of

elementary particles rather than building formal mathematical

structures, in a form that will be comprehensible to mathemati-

cians. Rigorous definitions and arguments are presented as far as they are available, but

the text proceeds on a more informal level when necessary, with due care in identifying

the difficulties.

The book begins with a review of classical physics and quantum mechanics, then

proceeds through the construction of free quantum fields to the perturbation-theoretic

development of interacting field theory and renormalization theory, with emphasis

on quantum electrodynamics. The final two chapters present the functional integral

approach and the elements of gauge field theory, including the Salam–Weinberg model

of electromagnetic and weak interactions.

For additional information

and updates on this book, visit

www.ams.org/bookpages/surv-149

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