Two-body Dirac equation for semirelativistic quarks

Journal Article · Sun Nov 14 23:00:00 EST 1982 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.26.2902· OSTI ID:6573712

Childers, R W

A semirelativistic quark model for mesons is proposed, based on a comprehensive treatment of the two-body Dirac equation introduced by Breit in 1929. Sixteen-component eigenstates of J/sup 2/, J/sub 3/, and parity are constructed. They are used to obtain radial equations for the most general local, nonderivative interaction Hamiltonian of order v/sup 2//c/sup 2/ containing both scalar and four-vector terms. The Breit interaction is a special case of this interaction Hamiltonian, and the radial equations are considered first for that case. It has been known since 1930 that there is an ambiguity associated with the Breit equation. It arises because there are two different ways to reduce the Breit equation to four-component form. In one method the Breit interaction is regarded as a perturbation and in the other it is not. Only the first method gives correct results. This ambiguity is resolved by a consideration of the radial equations for the Breit equation. In addition, explicit solutions of the radial equations to order ..cap alpha../sup 4/ are given for hydrogen and positronium. The conclusion is that the two-body Dirac equation is unambiguous and correct to order ..cap alpha../sup 4/ in QED. The radial equations are used next in the context of QCD to determine which of the 24 possible combinations of scalar and vector potentials considered can give rise to quark confinement in a normalized theory. If the higher-order potentials are no larger than the zero-order potentials in magnitude, we show that there are only two possible forms for the confinement interaction: (1) the scalar interaction S(r)(1-rxalpha-arrow-right/sub 1/rxalpha-arrow-right/sub 2/)..beta../sub 1/..beta../sub 2/ and (2) the combined scalar-vector interaction (V(r)+S(r)..beta../sub 1/..beta../sub 2/)(1-rxalpha-arrow-right/sub 1/ralpha-arrow-right/sub 2/) where S> or =V for large r.

• Research Organization: Department of Physics, University of Tennessee, Knoxville, Tennessee 37996
• OSTI ID: 6573712
• Journal Information: Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 26:10; ISSN PRVDA
• Country of Publication: United States
• Language: English

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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOSONS
COMPOSITE MODELS
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
EIGENSTATES
ELECTRODYNAMICS
ELEMENTARY PARTICLES
ENERGY RANGE
EQUATIONS
FIELD THEORIES
HADRONS
HAMILTONIANS
MANY-BODY PROBLEM
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MESONS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE MODELS
POSTULATED PARTICLES
POTENTIALS
QUANTUM CHROMODYNAMICS
QUANTUM ELECTRODYNAMICS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
QUARK MODEL
QUARKS
RELATIVISTIC RANGE
SCALAR FIELDS
TWO-BODY PROBLEM
VECTOR FIELDS
WAVE EQUATIONS