Nonperturbative solution of two-body Dirac equations for quantum electrodynamics and related field theories

Journal Article · Tue Dec 01 00:00:00 EST 1992 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.46.5117· OSTI ID:7030300

Crater, H W ^[1]; Becker, R L; Wong, C Y ^[2]; Van Alstine, P ^[3]

---

1. The University of Tennessee Space Institute, Tullahoma, Tennessee 37388 (United States)
2. Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6373 (United States)
3. 12474 Sunny Glen Drive, Moorpark, California 93021 (United States)

In quark-model calculations of the meson spectrum, fully covariant two-body Dirac equations dictated by Dirac's relativistic constraint mechanics gave a good fit to the entire meson mass spectrum (excluding flavor mixing) with constituent world scalar and vector potentials depending on just one or two parameters. In this paper, we investigate the properties of these equations that made them work so well by solving them numerically for quantum electrodynamics (QED) and related field theories. The constraint formalism generates a relativistic quantum mechanics defined by two coupled Dirac equations on a 16-component wave function which contain Lorentz-covariant constituent potentials that are initially undetermined. An exact Pauli reduction leads to a second-order relativistic Schroedinger-like equation for a reduced eight-component wave function determined by an effective interaction---the quasipotential. We first determine perturbatively to lowest order the relativistic quasipotential for the Schroedinger-like equation by comparing that form with one derived from the Bethe-Salpeter equation. Insertion of this perturbative information into the minimal interaction structures of the two-body Dirac equations then completely determines their interaction structures.

• DOE Contract Number: AC05-84OR21400
• OSTI ID: 7030300
• Journal Information: Physical Review, D (Particles Fields); (United States), Vol. 46:11; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
MESON SPECTROSCOPY
QUANTUM ELECTRODYNAMICS
DIRAC EQUATION
BETHE-SALPETER EQUATION
BOUND STATE
ELECTRON-POSITRON INTERACTIONS
LORENTZ TRANSFORMATIONS
MASS SPECTRA
PERTURBATION THEORY
QUANTUM MECHANICS
QUARK MODEL
RELATIVITY THEORY
SCALAR FIELDS
TWO-BODY PROBLEM
VECTOR FIELDS
WAVE EQUATIONS
WAVE FUNCTIONS
COMPOSITE MODELS
DIFFERENTIAL EQUATIONS
ELECTRODYNAMICS
EQUATIONS
FIELD THEORIES
FUNCTIONS
GENERAL RELATIVITY THEORY
INTERACTIONS
LEPTON-LEPTON INTERACTIONS
MANY-BODY PROBLEM
MATHEMATICAL MODELS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE INTERACTIONS
PARTICLE MODELS
QUANTUM FIELD THEORY
SPECTRA
SPECTROSCOPY
TRANSFORMATIONS
662220* - Quantum Electrodynamics- (1992-)
661100 - Classical & Quantum Mechanics- (1992-)