文档介绍：THE SCHWINGER ACTION PRINCIPLE
AND EFFECTIVE ACTION
This book is an introduction to the Schwinger action principle in quan-
tum mechanics and quantum field theory, with applications to a variety of
different models, not only those of interest to particle physics. The book
begins with a brief review of the action principle in classical mechan-
ics and classical field theory. It then moves on to quantum field theory,
focusing on the effective action method. This is introduced as simply as
possible by using the zero-point energy of the simple harmonic oscilla-
tor as the starting point. This allows the utility of the method, and the
process of regularization and renormalization of quantum field theory,
to be demonstrated with a minimum of formal development. The book
concludes with a plete definition of the effective action, and
demonstrates how the provisional definition used earlier is the first term
in the systematic loop expansion.
Several applications of the Schwinger action principle are given,
including Bose–Einstein condensation, the Casimir effect, and trapped
Fermi gases. The renormalization of interacting scalar field theory is
presented to two-loop order. This book will interest graduate students
and researchers in theoretical physics who are familiar with quantum
mechanics.
David Toms is Reader in Mathematical Physics in the School of Math-
ematics and Statistics at Newcastle University. Prior to joining New-
castle University, Dr. Toms was a NATO Science Fellow at Imperial
College London, and a postdoctoral Fellow at the University of Wisconsin-
Milwaukee. His research interests include the formalism of quantum field
theory and its applications, and his most recent interests are centred
around Kaluza–Klein theory, based on the idea that there are extra spatial
dimensions beyond the three obvious ones.
CAMBRIDGE MONOGRAPHS ON MATHEMATICAL PHYSICS
General Editors: P. V. Landshoff, D. R. Nelson, S. Weinberg
S. J. Aarseth Gravitational N-B