Extension of the Conventional Framework of Local Quantum Field Theory and the Description of Resonances
to incorporate correctly the instability property into the theory,
to get the consistency with an experimental fact that in asymptotic space — time regions there are only observed free stable particles.
The aim of this lecture is to discuss the applicability to the description of strongly unstable objects the field operator ϕ(x;s), with continuous spectrum of asymptotic masses.
KeywordsField Operator Spectral Function Unstable Particle Elementary Object Asymptotic Field
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- 1.The unstable particles were mainly studied in the framework of Ŝ-matrix theory, where the Peierl’s concept of complex pole on second Rieman sheet of the propagator has been used. Below we list some papers, from “classical” period 1958 — 1963, where there were made many attempts to find the place of unstable particles in general framework of relativistic local QFT: a) P. T. Matthews, A. Salam, Phys. Rev. 112, 283 (1958); 115, 1079 (1959).MathSciNetADSMATHGoogle Scholar
- As basic paper for field-theoretic understanding of the properties of unstable state should be quoted N. S. KRYLOV and B. A. FOCK, JETF 17, 93 (1947). These ideas were elaborated further by L. A. Khalfin in his papers (see DAN SSSR and JETF; 1956–1969).Google Scholar
- a).V. Glaser and G. Källén, Nucl. Phys. 2, 706 (1957).Google Scholar
- d).W. Jaus, Helv. Phys. Acta 39, 617 (1966).Google Scholar
- 4.a)A. L. Licht, Maryland Thesis 1963.Google Scholar
- c).See also A. S. Wightman, Cargese Summer School Lectures, Corsica, 1964.Google Scholar
- 5. a)
- 7.See also J. Lukierski, “Field Theory Describing Interacting Two-Particle Subsystems, I. General Formalism”, Nuovo Cim.; in press.Google Scholar
- 8.Lukierski, J., Proceedings of Balaton Seminar on Hadrons, September 1968, publ. Acta Phys. Hungarica, 1969.Google Scholar
- a).R. Jost, “General Theory of Quantized Fields”, Providence, R. I. 1965.Google Scholar
- b).R. F. Streater and A. S. Wightman, “PCT, Spin and Statistics, and All That”, Bejamin Inc., New York 1965.Google Scholar
- 10. a)
- 12.See [4a-b] and . The proof of generalized LSZ asymptotic condition has been given by W. KARWOWSKI and N. SZNAJDER, Acta Phys. Polon., in press: see also W. KARWOWSKI, J. Lukierski and N. SZNAJDER, Nuovo Cim., to be published.Google Scholar
- 13.L. Streit, Helv. Phys. Acta 39, 65 (1965).Google Scholar
- 14.R. A. Brandt and O. W. Greenberg, University of Maryland, preprint No. 817, June 1968.Google Scholar
- 20.See , the second reference.Google Scholar
- 24.It should be mentioned, that in order to get the Regge behaviour the spectral function Λ2(s) should tend to zero for large values of s → ∞, but can be non-integrable.Google Scholar
- 26. a)L. D. Faddeev, Mathematical Problems of Quantum Theory of Scattering of a Three-Particle State, publ. Steklov Institute, No. 39 (1963).Google Scholar