General Principles of Quantum Field Theory

1. Front Matter

   Pages i-xix

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2. Elements of Functional Analysis and the Theory of Functions

   1. Front Matter

      Pages 1-2

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   2. Preliminaries on Functional Analysis

      • N. N. Bogolubov, A. A. Logunov, A. I. Oksak, I. T. Todorov, G. G. Gould

      Pages 3-45

   3. The Technique of Generalized Functions

      • N. N. Bogolubov, A. A. Logunov, A. I. Oksak, I. T. Todorov, G. G. Gould

      Pages 46-117

   4. Lorentz-Covariant Generalized Functions

      • N. N. Bogolubov, A. A. Logunov, A. I. Oksak, I. T. Todorov, G. G. Gould

      Pages 118-169

   5. The Jost-Lehmann-Dyson Representation

      • N. N. Bogolubov, A. A. Logunov, A. I. Oksak, I. T. Todorov, G. G. Gould

      Pages 170-196

   6. Analytic Functions of Several Complex Variables

      • N. N. Bogolubov, A. A. Logunov, A. I. Oksak, I. T. Todorov, G. G. Gould

      Pages 197-230

3. Relativistic Quantum Systems

   1. Front Matter

      Pages 231-232

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   2. Algebra of Observables and State Space

      • N. N. Bogolubov, A. A. Logunov, A. I. Oksak, I. T. Todorov, G. G. Gould

      Pages 233-269

   3. Relativistic Invariance in Quantum Theory

      • N. N. Bogolubov, A. A. Logunov, A. I. Oksak, I. T. Todorov, G. G. Gould

      Pages 270-317

4. Local Quantum Fields and Wightman Functions

   1. Front Matter

      Pages 318-320

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   2. The Wightman Formalism

      • N. N. Bogolubov, A. A. Logunov, A. I. Oksak, I. T. Todorov, G. G. Gould

      Pages 321-358

   3. Analytic Properties of Wightman Functions in Coordinate Space

      • N. N. Bogolubov, A. A. Logunov, A. I. Oksak, I. T. Todorov, G. G. Gould

      Pages 359-416

   4. Fields in an Indefinite Metric

      • N. N. Bogolubov, A. A. Logunov, A. I. Oksak, I. T. Todorov, G. G. Gould

      Pages 417-449

   5. Examples: Explicitly Soluble Two-Dimensional Models

      • N. N. Bogolubov, A. A. Logunov, A. I. Oksak, I. T. Todorov, G. G. Gould

      Pages 450-483

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

   1. Front Matter

      Pages 484-485

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   2. Haag-Ruelle Scattering Theory

      • N. N. Bogolubov, A. A. Logunov, A. I. Oksak, I. T. Todorov, G. G. Gould

      Pages 486-502

   3. Lehmann-Symanzik-Zimmermann Formalism

      • N. N. Bogolubov, A. A. Logunov, A. I. Oksak, I. T. Todorov, G. G. Gould

      Pages 503-529

   4. The S-Matrix Method

      • N. N. Bogolubov, A. A. Logunov, A. I. Oksak, I. T. Todorov, G. G. Gould

      Pages 530-545

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

   1. Front Matter

      Pages 546-547

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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.

• Cross section
• Dirac equation
• Observable
• Quark
• Second quantization
• classification
• statistics

• 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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