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Introduction to algebraic and constructive quantum field theory. (English) Zbl 0760.46061
Princeton Series in Physics. Princeton, NJ: Princeton University Press. xvii, 291 p. (1992).
Much of the quantum field theory is of a very general character independent of the nature of space-time. Thus a universal formalism applies whether or not there exists an underlying space in the usual geometrical sense. This book deals with this universal part of quantum field theory which depends only on the underlying complex Hilbert space.
The main topics are:
— The universal free boson field.
— The universal fermion field along parallel lines.
— General properties of universal fields.
— Absolute continuity of distributions in function spaces, unitary implementability.
— \(C^*\)-algebras associated with the underlying symplectic or orthogonal structures.
— Quantization of wave equations.
— Renormalized local products of boson fields.
— Nonlinear scalar field in two space-time dimensions, methods of constructive quantum field theory.
Reviewer: A.Wehrl (Wien)

46N50 Applications of functional analysis in quantum physics
46L60 Applications of selfadjoint operator algebras to physics
46-02 Research exposition (monographs, survey articles) pertaining to functional analysis
81T05 Axiomatic quantum field theory; operator algebras
81T08 Constructive quantum field theory
81-02 Research exposition (monographs, survey articles) pertaining to quantum theory