A detailed study of nonperturbative solutions of two-body Dirac equations

Technical Report · Tue Dec 01 00:00:00 EST 1992

DOI:https://doi.org/10.2172/6832686· OSTI ID:6832686

Crater, H. W.; Becker, R. L.; Wong, C. Y.; Van Alstine, P.

In quark model calculations of the meson spectrums fully covariant two-body Dirac equations dictated by Dirac's relativistic constraint mechanics gave a good fit to the entire meson mass spectrum for light quark mesons as well as heavy quark mesons 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 sixteen 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. Then we give a procedure for constructing the full sixteen component solution to our coupled first-order Dirac equations from a solution of the second order equation for the reduced wave function. Next, we show that a perturbative treatment of these equations yields the standard spectral results for QED and related interactions.

• Research Organization: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: USDOE; USDOE, Washington, DC (United States)
• DOE Contract Number: AC05-84OR21400
• OSTI ID: 6832686
• Report Number(s): ORNL/TM-12122; ON: DE93004794
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIRAC EQUATION
NUMERICAL SOLUTION
MESONS
TWO-BODY PROBLEM
BETHE-SALPETER EQUATION
MASS SPECTRA
QUANTUM ELECTRODYNAMICS
QUARK MODEL
SCATTERING
SCHROEDINGER EQUATION
WAVE FUNCTIONS
BOSONS
COMPOSITE MODELS
DIFFERENTIAL EQUATIONS
ELECTRODYNAMICS
ELEMENTARY PARTICLES
EQUATIONS
FIELD THEORIES
FUNCTIONS
HADRONS
MANY-BODY PROBLEM
MATHEMATICAL MODELS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE MODELS
QUANTUM FIELD THEORY
SPECTRA
WAVE EQUATIONS
662110* - General Theory of Particles & Fields- Theory of Fields & Strings- (1992-)
661100 - Classical & Quantum Mechanics- (1992-)
662220 - Quantum Electrodynamics- (1992-)
662420 - Properties of Mesons & Meson Resonances- (1992-)