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General Principles of Quantum Field Theory

  • Book
  • © 1990


Part of the book series: Mathematical Physics and Applied Mathematics (MPAM, volume 10)

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About this book

The majority of the "memorable" results of relativistic quantum theory were obtained within the framework of the local quantum field approach. The explanation of the basic principles of the local theory and its mathematical structure has left its mark on all modern activity in this area. Originally, the axiomatic approach arose from attempts to give a mathematical meaning to the quantum field theory of strong interactions (of Yukawa type). The fields in such a theory are realized by operators in Hilbert space with a positive Poincare-invariant scalar product. This "classical" part of the axiomatic approach attained its modern form as far back as the sixties. * It has retained its importance even to this day, in spite of the fact that nowadays the main prospects for the description of the electro-weak and strong interactions are in connection with the theory of gauge fields. In fact, from the point of view of the quark model, the theory of strong interactions of Wightman type was obtained by restricting attention to just the "physical" local operators (such as hadronic fields consisting of ''fundamental'' quark fields) acting in a Hilbert space of physical states. In principle, there are enough such "physical" fields for a description of hadronic physics, although this means that one must reject the traditional local Lagrangian formalism. (The connection is restored in the approximation of low-energy "phe­ nomenological" Lagrangians.

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Table of contents (17 chapters)

  1. Elements of Functional Analysis and the Theory of Functions

  2. Relativistic Quantum Systems

  3. Local Quantum Fields and Wightman Functions

  4. Collision Theory. Axiomatic Theory of the S-Matrix

  5. Causality and the Spectral Property: The Origins of the Analytic Properties of the Scattering Amplitude

Editors and Affiliations

  • U.S.S.R. Academy of Sciences and Moscow State University, U.S.S.R.

    N. N. Bogolubov, A. A. Logunov

  • Institute for High Energy Physics, Moscow, U.S.S.R.

    A. I. Oksak

  • Bulgarian Academy of Sciences and Bulgarian Institute for Nuclear Research and Nuclear Energy, Sofia, Bulgaria

    I. T. Todorov

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