Two-body Dirac equations for particles interacting through world scalar and vector potentials

Journal Article · Sun Nov 15 00:00:00 EST 1987 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.36.3007· OSTI ID:5582767

Crater, H W; Van Alstine, P

In a recent Letter, we used ''two-body Dirac equations'' to make the naive quark model fully relativistic. In this paper, we apply Dirac's constraint mechanics and supersymmetry not to a string but instead to a system of two spinning particles to derive the two coupled Dirac equations that govern the quantum mechanics of two spin-1/2 particles interacting through world scalar and vector potentials. Along the way, we demonstrate that our equations are compatible, that the scalar and vector interaction structures contribute separately to compatibility when both are present, and that compatibility persists even in the presence of relative-momentum-dependent interactions. We show that extrapolation of supersymmetries associated with the ordinary single-particle Dirac equation to the interacting two-body system eliminates spin complications and reduces the compatibility problem to that of the corresponding spinless system. In addition, supersymmetry introduces physically important nonperturbative recoil effects that contribute to the correct perturbative spectrum while rendering nonsingular certain singular terms of standard semirelativistic approximations. This eliminates the need for singularity-softening parameters or finite particle sizes in phenomenological applications. In order to make clear the underlying structure of our equations, we also derive the corresponding coupled Dirac or Klein-Gordon equations that govern a system of two particles, one or neither of which has spin.

• Research Organization: The University of Tennessee Space Institute, Tullahoma, Tennessee 37388
• OSTI ID: 5582767
• Journal Information: Phys. Rev. D; (United States), Vol. 36:10
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
DIRAC EQUATION
TWO-BODY PROBLEM
BETHE-SALPETER EQUATION
CHIRAL SYMMETRY
KLEIN-GORDON EQUATION
PARTICLE INTERACTIONS
PERTURBATION THEORY
QUANTUM FIELD THEORY
QUANTUM MECHANICS
QUARKS
RECOILS
SCALAR FIELDS
SPIN
SUPERSYMMETRY
VECTOR FIELDS
WAVE EQUATIONS
ANGULAR MOMENTUM
DIFFERENTIAL EQUATIONS
ELEMENTARY PARTICLES
EQUATIONS
FIELD THEORIES
INTERACTIONS
MANY-BODY PROBLEM
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE PROPERTIES
POSTULATED PARTICLES
SYMMETRY
645400* - High Energy Physics- Field Theory