NONRENORMALIZABILITY AND THE SHORTRANGE FORCE IN SOME FIELD THEORETIC MODELS

Journal Article · Mon Apr 27 04:00:00 EDT 1964 · Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D

DOI:https://doi.org/10.1103/PhysRev.134.B448· OSTI ID:4031895

Sawyer, R F

Bethe-Salpeter equations for the scattering Green's functions are discussed in some nonrenormalizable models. The models involve the multiple exchanges of pairs of Dirac particles, coupled to the scattering particles by a fourFermi interaction. The Green's function is constructed from a Bethe-Salpeter scattering wave function. For certain forms of coupling the forces are repulsive at short distances and analogous to potentials in a nonrelntivistic scattering problem that behave as r/sup -6/ at the origin. In these cases there is a unique, well defined, and Fourier transformable solution for the Green's function in space-time; and the scattering amplitude exists. A class of terms corresponding to delta-function potentials may be included in the interaction kernel without changing the solution. In a case with zero-mass particles and zero total energy an exact solution for the scattering amplitude is obtained. (auth)

• Research Organization: Univ. of Wisconsin, Madison
• NSA Number: NSA-18-018769
• OSTI ID: 4031895
• Journal Information: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D, Journal Name: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D Vol. Vol: 134; ISSN PHRVA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

BEHAVIOR
BETHE-SALPETER EQUATION
CONFIGURATION
COUPLING
DIRAC EQUATIONS
ENERGY
FERMIONS
FIELD THEORY
FOURIER ANALYSIS
GREEN FUNCTION
INTERACTIONS
MASS
MATHEMATICS
OSCILLATIONS
PARTICLE MODELS
PARTICLES
PHYSICS
QUANTUM MECHANICS
RELATIVITY THEORY
SCATTERING
SCATTERING AMPLITUDE