TY - JOUR

T1 - Exact three-dimensional reduction of the Bethe-Salpeter equation

AU - Zmora, I.

AU - Gersten, A.

PY - 1977/1/1

Y1 - 1977/1/1

N2 - The partial-wave Bethe-Salpeter equation in the ladder approximation is converted into a set of two one-dimensional equations. The resulting reduced equations determine two off-energy-shell, on-mass-shell amplitudes, one for the scattering of two positive-energy and the other for two negative-energy particles. The connection between the potentials of the reduced equations and the many-particle intermediate states is displayed by their series expansion. Two versions of the equations which are convenient for numerical computations are also obtained, and one of them is a one-channel equation which involves only the physical amplitude for the scattering of two positive-energy particles. The potentials are determined by auxiliary equations which are two dimensional but nonsingular and exactly solvable by standard numerical methods. One of the results of the derivation of the reduced equations is a set of reduction relations which express the off-mass-shell amplitude as a functional of a restricted shell amplitude.

AB - The partial-wave Bethe-Salpeter equation in the ladder approximation is converted into a set of two one-dimensional equations. The resulting reduced equations determine two off-energy-shell, on-mass-shell amplitudes, one for the scattering of two positive-energy and the other for two negative-energy particles. The connection between the potentials of the reduced equations and the many-particle intermediate states is displayed by their series expansion. Two versions of the equations which are convenient for numerical computations are also obtained, and one of them is a one-channel equation which involves only the physical amplitude for the scattering of two positive-energy particles. The potentials are determined by auxiliary equations which are two dimensional but nonsingular and exactly solvable by standard numerical methods. One of the results of the derivation of the reduced equations is a set of reduction relations which express the off-mass-shell amplitude as a functional of a restricted shell amplitude.

UR - http://www.scopus.com/inward/record.url?scp=35949033439&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.16.3581

DO - 10.1103/PhysRevD.16.3581

M3 - Article

AN - SCOPUS:35949033439

SN - 1550-7998

VL - 16

SP - 3581

EP - 3595

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

IS - 12

ER -