Bound-state problem in the light-front Tamm-Dancoff approximation: Numerical study in 1+1 dimensions

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

DOI:https://doi.org/10.1103/PhysRevD.46.4580· OSTI ID:6950065

Harindranath, A; Perry, R J ^[1]; Shigemitsu, J ^[2]

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1. Department of Physics, The Ohio State University, Columbus, Ohio 43210 (United States)
2. Physics Department, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215 (United States) DESY, Theory Group, Notkestrasse 85, D-2000, Hamburg 52 (Germany)

Numerical solutions to the two-fermion bound-state problem in the (1+1)-dimensional Yukawa model are presented within the lowest-order light-front Tamm-Dancoff approximation (i.e., keeping only two-fermion and two-fermion--one-boson sectors). Our motivation is twofold. First, we want to understand the dynamics of the model from the very-weak-coupling domain, where the system is governed by nonrelativistic dynamics, to moderate and strong-coupling domains where retardation and self-energy effects become important. Second, we want to develop techniques for solving coupled Tamm-Dancoff integral equations, in particular, methods that can be generalized to higher-order Tamm-Dancoff approximations. To achieve the first goal we first simplify the problem considerably (from a numerical point of view) by the explicit elimination of the higher Fock-space sector. The resulting integral equation, whose kernel depends upon the invariant mass of the state, is solved for the coupling constant, for a given set of the invariant mass and fermion and boson mass parameters. To achieve the second goal we solve the coupled set of equations using both basis functions and direct-discretization techniques. Results from these more general techniques are compared with the explicit-elimination method.

• DOE Contract Number: AC02-76ER01545; AC02-89ER40509
• OSTI ID: 6950065
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 46:10; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
662340 -- Hadron Interactions-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOSONS
BOUND STATE
COUPLING CONSTANTS
ENERGY
EQUATIONS
FERMIONS
INTEGRAL EQUATIONS
LIGHT CONE
MANY-BODY PROBLEM
MASS
MATHEMATICAL MODELS
NUCLEAR MODELS
NUCLEAR POTENTIAL
PARTICLE MODELS
POTENTIALS
QUANTIZATION
RENORMALIZATION
SELF-ENERGY
SPACE-TIME
STRONG-COUPLING MODEL
TAMM-DANCOFF METHOD
TWO-BODY PROBLEM
TWO-DIMENSIONAL CALCULATIONS
WEAK-COUPLING MODEL
YUKAWA POTENTIAL