Renormalization of Tamm-Dancoff integral equations

Journal Article · Tue Dec 15 04:00:00 EST 1992 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.46.5479· OSTI ID:6990844

van de Sande, B; Pinsky, S S ^[1]

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1. Department of Physics, The Ohio State University, 174 West 18th Avenue, Columbus, Ohio 43210 (United States)

During the last few years, interest has arisen in using light-front Tamm-Dancoff field theory to describe relativistic bound states for theories such as QCD. Unfortunately, difficult renormalization problems stand in the way. We introduce a general, nonperturbative approach to renormalization that is well suited for the ultraviolet and, presumably, the infrared divergences found in these systems. We reexpress the renormalization problem in terms of a set of coupled inhomogeneous integral equations, the counterterm equation.'' The solution of this equation provides a kernel for the Tamm-Dancoff integral equations which generates states that are independent of any cutoffs. We also introduce a Rayleigh-Ritz approach to numerical solution of the counterterm equation. Using our approach to renormalization, we examine several ultraviolet-divergent models. Finally, we use the Rayleigh-Ritz approach to find the counterterms in terms of allowed operators of a theory.

• OSTI ID: 6990844
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 46:12; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

662230* -- Quantum Chromodynamics-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOUND STATE
CALCULATION METHODS
EIGENVALUES
EQUATIONS
FIELD THEORIES
GENERAL RELATIVITY THEORY
HAMILTONIANS
INFRARED DIVERGENCES
INTEGRAL EQUATIONS
MATHEMATICAL OPERATORS
QUANTUM CHROMODYNAMICS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
RELATIVITY THEORY
RENORMALIZATION
RITZ METHOD
TAMM-DANCOFF METHOD
ULTRAVIOLET DIVERGENCES