Complete Reduction of Fermion anti-Fermion Bethe-Salpeter Equation with Static Kernel
May, 1975
40 pages
Published in:
- Annals Phys. 96 (1976) 261
Report number:
- Print-75-0560 (JOHNS HOPKINS)
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Abstract: (Elsevier)
The Bethe-Salpeter (BS) equation for a spin - 1 2 fermion-antifermion bound system is considered for the case in which the kernel is static and is the fourth component (i.e., three-scalar part) of a vector potential. Relative time (or relative energy) dependence can be eliminated easily. The 16 BS bispinor amplitudes are reexpressed in the usual way in terms of corresponding tensor amplitudes which satisfy 16 coupled integrodifferential equations. If Lorentz-, parity-, and charge-conjugation invariance are used, these equations can be reduced through a sequence of transformations to single eigenvalue equations, involving scalar and three-vector wavefunctions for singlet and triplet states, respectively. The effective Hamiltonians obtained in these equations are correct to all orders in the coupling constant and have a simple structure, consisting in general of a scalar, a spin-orbit, and a tensor part, which are explicitly exhibited.- QUANTUM MECHANICS: RELATIVISTIC
- PERTURBATION THEORY
- FERMION FERMION: BOUND STATE
- FERMION: ANTIPARTICLE
- BETHE-SALPETER EQUATION
- MATHEMATICS
- ELECTRON POSITRON: ATOM
- NUMERICAL CALCULATIONS
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