S-matrix renormalization in effective theories

Journal Article · Sun Jan 15 04:00:00 EST 2006 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.73.0· OSTI ID:20795764

Semenov-Tian-Shansky, K ^[1]; Vereshagin, A ^[2]; Vereshagin, V ^[3]

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1. Departement de Physique, Universite de Liege au Sart Tilman, B5a, B4000 Liege 1 (Belgium)
2. Institute of Physics and Technology, Allegaten 55, N5007 Bergen (Norway)
3. Theoretical Physics Department, Institute of Physics, St. Petersburg State University, St. Petersburg, Petrodvoretz, 198504 (Russian Federation)

This is the fifth paper in the series devoted to explicit formulation of the rules needed to manage an effective field theory of strong interactions in S-matrix sector. We discuss the principles of constructing the meaningful perturbation series and formulate two basic ones: uniformity and summability. Relying on these principles, one obtains the bootstrap conditions which restrict the allowed values of the physical (observable) parameters appearing in the extended perturbation scheme built for a given localizable effective theory. The renormalization prescriptions needed to fix the finite parts of counterterms in such a scheme can be divided into two subsets: minimal, needed to fix the S-matrix, and nonminimal, for eventual calculation of Green functions; in this paper we consider only the minimal one. In particular, it is shown that, in theories with the asymptotic behavior governed by known Regge intercepts, the system of independent renormalization conditions only contains those fixing the counterterm vertices with n{<=}3 lines, while other prescriptions are determined by self-consistency requirements. Moreover, the prescriptions for n{<=}3 cannot be taken arbitrarily: an infinite number of bootstrap conditions should be respected. The concept of localizability, introduced and explained in this article, is closely connected with the notion of resonance in the framework of perturbative quantum field theory. We discuss this point and, finally, compare the cornerstones of our approach with the philosophy known as ''analytic S-matrix.''.

• OSTI ID: 20795764
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 2 Vol. 73; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOOTSTRAP MODEL
COMPARATIVE EVALUATIONS
DISTURBANCES
GREEN FUNCTION
PERTURBATION THEORY
QUANTUM FIELD THEORY
RENORMALIZATION
RESONANCE
S MATRIX
STRONG INTERACTIONS