The authors present a rigorous treatment of the first principles
of the algebraic and analytic core of quantum field theory. Their
aim is to correlate modern mathematical theory with the explanation
of the observed process of particle production and of particle-wave
duality that heuristic quantum field theory provides. Many topics
are treated here in book form for the first time, from the origins
of complex structures to the quantization of tachyons and domains
of dependence for quantized wave equations. This work begins with a
comprehensive analysis, in a universal format, of the structure and
characterization of free fields, which is illustrated by
applications to specific fields. Nonlinear local functions of both
free fields (or Wick products) and interacting fields are
established mathematically in a way that is consistent with the
basic physical constraints and practice. Among other topics
discussed are functional integration, Fourier transforms in Hilbert
space, and implementability of canonical transformations. The
authors address readers interested in fundamental mathematical
physics and who have at least the training of an entering graduate
student. A series of lexicons connects the mathematical development
with the underlying physical motivation or interpretation. The
examples and problems illustrate the theory and relate it to the
scientific literature.
Originally published in 1992.
The Princeton Legacy Library uses the latest print-on-demand
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from the distinguished backlist of Princeton University Press.
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