Barry Simon's book both summarizes and introduces the remarkable
progress in constructive quantum field theory that can be attributed
directly to the exploitation of Euclidean methods. During the past two
years deep relations on both the physical level and on the level of the
mathematical structure have been either uncovered or made rigorous.
Connections between quantum fields and the statistical mechanics of
ferromagnets have been established, for example, that now allow one to
prove numerous inequalities in quantum field theory.
In the first part of the book, the author presents the Euclidean methods
on an axiomatic level and on the constructive level where the
traditional results of the P(Ø)2 theory are translated into the new
language. In the second part Professor Simon gives one of the approaches
for constructing models of non-trivial, two-dimensional Wightman
fields--specifically, the method of correlation inequalities. He
discusses other approaches briefly.
Drawn primarily from the author's lectures at the Eidenössiehe
Technische Hochschule, Zurich, in 1973, the volume will appeal to
physicists and mathematicians alike; it is especially suitable for those
with limited familiarity with the literature of this very active field.
Originally published in 1974.
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