Ebook: General Principles of Quantum Field Theory

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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Content:
Front Matter....Pages i-xix
Front Matter....Pages 1-2
Preliminaries on Functional Analysis....Pages 3-45
The Technique of Generalized Functions....Pages 46-117
Lorentz-Covariant Generalized Functions....Pages 118-169
The Jost-Lehmann-Dyson Representation....Pages 170-196
Analytic Functions of Several Complex Variables....Pages 197-230
Front Matter....Pages 231-232
Algebra of Observables and State Space....Pages 233-269
Relativistic Invariance in Quantum Theory....Pages 270-317
Front Matter....Pages 318-320
The Wightman Formalism....Pages 321-358
Analytic Properties of Wightman Functions in Coordinate Space....Pages 359-416
Fields in an Indefinite Metric....Pages 417-449
Examples: Explicitly Soluble Two-Dimensional Models....Pages 450-483
Front Matter....Pages 484-485
Haag-Ruelle Scattering Theory....Pages 486-502
Lehmann-Symanzik-Zimmermann Formalism....Pages 503-529
The S-Matrix Method....Pages 530-545
Front Matter....Pages 546-547
Analyticity with respect to Momentum Transfer and Dispersion Relations....Pages 548-573
Analytic Properties of the Four-Point Green’s Function....Pages 574-607
Consequences for High-Energy Elementary Processes....Pages 608-625
Back Matter....Pages 626-695

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Content:
Front Matter....Pages i-xix
Front Matter....Pages 1-2
Preliminaries on Functional Analysis....Pages 3-45
The Technique of Generalized Functions....Pages 46-117
Lorentz-Covariant Generalized Functions....Pages 118-169
The Jost-Lehmann-Dyson Representation....Pages 170-196
Analytic Functions of Several Complex Variables....Pages 197-230
Front Matter....Pages 231-232
Algebra of Observables and State Space....Pages 233-269
Relativistic Invariance in Quantum Theory....Pages 270-317
Front Matter....Pages 318-320
The Wightman Formalism....Pages 321-358
Analytic Properties of Wightman Functions in Coordinate Space....Pages 359-416
Fields in an Indefinite Metric....Pages 417-449
Examples: Explicitly Soluble Two-Dimensional Models....Pages 450-483
Front Matter....Pages 484-485
Haag-Ruelle Scattering Theory....Pages 486-502
Lehmann-Symanzik-Zimmermann Formalism....Pages 503-529
The S-Matrix Method....Pages 530-545
Front Matter....Pages 546-547
Analyticity with respect to Momentum Transfer and Dispersion Relations....Pages 548-573
Analytic Properties of the Four-Point Green’s Function....Pages 574-607
Consequences for High-Energy Elementary Processes....Pages 608-625
Back Matter....Pages 626-695
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