QED test of a Bethe-Salpeter solution method

Journal Article · Thu Feb 14 23:00:00 EST 1991 · Physical Review, D (Particles Fields); (USA)

DOI:https://doi.org/10.1103/PhysRevD.43.1393· OSTI ID:5753748

Connell, J H ^[1]

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1. Springfield Technical Community College, Armory Square, Springfield, Massachusetts 01105 (US)

A method is described of solving Bethe-Salpeter equations for spin-1/2 particles using a standard quasipotential approximation with a correction series. A three-dimensional, 16-component bound-state equation is obtained whose form is different from the Breit equation. The equation has two equivalent first-order forms which show each particle obeying a Dirac equation in the presence of the other. The formalism also reconstitutes the four-dimensional bound-state vertex function from the three-dimensional wave function. The method is tested on positronium and the hydrogen atom, using a single-photon-exchange kernel in the Coulomb gauge. In the bound-state equation, in addition to the Coulomb potential and Breit interaction, the formalism gives a subtracted box potential (1/2{ital E}){alpha}{sup 2}/{ital r}{sup 2} where {ital E} is the mass of the bound state. With this term included, the energy levels (fine structure and hyperfine structure) are correct to order {alpha}{sup 4}. The reconstituted bound-state vertex function, when substituted in Feynman triangle diagrams, gives the lowest-order atomic dipole transition amplitudes correctly.

• OSTI ID: 5753748
• Journal Information: Physical Review, D (Particles Fields); (USA), Journal Name: Physical Review, D (Particles Fields); (USA) Vol. 43:4; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

645201 -- High Energy Physics-- Particle Interactions & Properties-Theoretical-- General & Scattering Theory
645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ATOMS
BETHE-SALPETER EQUATION
BOUND STATE
COMPOSITE MODELS
DIAGRAMS
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
ELECTRODYNAMICS
ELEMENTS
ENERGY LEVELS
EQUATIONS
FEYNMAN DIAGRAM
FIELD THEORIES
FOUR-DIMENSIONAL CALCULATIONS
FUNCTIONS
GENERAL RELATIVITY THEORY
HYDROGEN
HYPERFINE STRUCTURE
MATHEMATICAL MODELS
NONMETALS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE MODELS
PERTURBATION THEORY
POSITRONIUM
QUANTUM ELECTRODYNAMICS
QUANTUM FIELD THEORY
QUARK MODEL
RELATIVITY THEORY
THREE-DIMENSIONAL CALCULATIONS
VERTEX FUNCTIONS
WAVE EQUATIONS
WAVE FUNCTIONS