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P(0)2 Euclidean (Quantum) Field Theory
Barry Simon
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Naturwissenschaften, Medizin, Informatik, Technik / Naturwissenschaften allgemein
Beschreibung
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.
The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
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Bochner's theorem, Hilbert space, Stone–Weierstrass theorem, Sobolev space, Monotonic function, Bounded set (topological vector space), Fock space, Infinitesimal generator (stochastic processes), Probability theory, Scalar field theory, Wick's theorem, Operator (physics), Lorentz covariance, Theorem, Axiom, Correlation function (quantum field theory), Lagrangian (field theory), Abelian von Neumann algebra, Riemann sum, Quantum mechanics, Cauchy's integral theorem, Minlos' theorem, Banach space, Mathematical induction, Monotone convergence theorem, Projection (linear algebra), Whitney extension theorem, Spectral theorem, Radon–Nikodym theorem, Fubini's theorem, Non-Euclidean geometry, Feynman–Kac formula, Theory, Expectation value (quantum mechanics), Mehler kernel, Statistical mechanics, Gaussian process, Perturbation theory, Quantum field theory, Nuclear space, Euclidean field, Characteristic function (probability theory), Laplace transform, Approximation theory, Bessel's inequality, Renormalization, Locally integrable function, Perturbation theory (quantum mechanics), Measure (mathematics), Euclidean space, Relativistic quantum mechanics, Norm (mathematics), Von Neumann algebra, Random variable, Heisenberg model (quantum), Central limit theorem, Constructive quantum field theory, Bessel function, Gaussian measure, Sign (mathematics), Field strength (theoretical physics), Schwinger function, Quantum electrodynamics, Markov random field, Rolle's theorem, Eigenfunction, Degeneracy (mathematics), Taylor's theorem, Orthonormal basis, Dirichlet boundary condition