On quantum electrodynamics of two-particle bound states containing spinless particles

• Published in: Foundations of physics Vol. 24; no. 2; pp. 273 - 296
• Main Author: OWEN, D. A
• Format: Journal Article
• Language: English
• Published: New York, NY Kluwer/Plenum 01.02.1994
• Subjects: BETHE-SALPETER EQUATION; Bound and unstable states; bethe-salpeter equations; BOUND STATE; CANONICAL TRANSFORMATIONS; ELECTRODYNAMICS; EQUATIONS; Exact sciences and technology; FIELD THEORIES; Field theory; FOLDY-WOUTHUYSEN TRANSFORM; General theory of fields and particles; MANY-BODY PROBLEM; Physics; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; QUANTUM ELECTRODYNAMICS; QUANTUM FIELD THEORY; SCALARS; Specific calculations; Specific theories and interaction models; particle systematics; The physics of elementary particles and fields; TRANSFORMATIONS 662220 > Quantum Electrodynamics > (1992-); TWO-BODY PROBLEM; Perturbation theory; Energy levels; Quantum electrodynamics; Propagator; Spinless particle; Scalar particle; Bound states; Bethe-Salpeter equation
• ISSN: 0015-9018; 1572-9516
• DOI: 10.1007/BF02313125

The authors develop here the general treatment arising from the Bethe-Salpeter equation for a two-particle bound system in which at least one of the particles is spinless. It is shown that a natural two-component formalism can be formulated for describing the propagators of scalar particles. This leads to a formulation of the Bethe-Salpeter equation in a form very reminiscent of the fermion-fermion case. It is also shown, that using this two-component formulation for spinless particles, the perturbation theory can be systematically developed in a manner similar to that of fermions. Quantum electrodynamics for scalar particles is then developed in the two component formalism, and the problem of bound states, in which one of the constituent particles is spinless, is examined by means of the means of the Bethe-Salpeter equation. For this case, the Bethe-Salpeter equation is cast into a form which is convenient to perform a Foldy-Woutyhuysen transformation which is carried out, keeping the lowest-order relativistic corrections to the nonrelativistic equation. The results are compared with the corresponding fermion-fermion case. It is shown, as might have been expected, that the only spin-independent terms that occur for the fermion-fermion system which do not occur for bound scalar particle cases, is the zitterbewegung contribution. The relevance of the above consideration for systems that are essentially bound by electromagnetic interactions, such as kaonic hydrogen, is discussed. 14 refs.