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.
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