Quantum field theory has been a great success for physics, but it is
difficult for mathematicians to learn because it is mathematically
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 mathematicians. 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.
Readership
Graduate students and research mathematicans interested in
mathematical physics, specifically, quantum field theory.