Two-Body Dirac Equation and Its Wave Function at the Origin

Details Two-Body Dirac Equation and Its Wave Function at the Origin Two-Body Dirac Equation and Its Wave Function at the Origin

1996-12-21

arxiv.org/abs/hep-ph/9612445v1

Physics

High Energy Physics

High Energy Physics - Phenomenology

LaTeX, 12 pages

Scientific paper

A relativistic equation is deduced for the bound state of two particles, by assuming a proper boundary condition for the propagation of the negative-energy states. It reduces to the (one-body)Dirac equation in the infinite limit of one of the constituent mass. It also has the symmetries to assure the existence of the anti-bound-state with the same mass. The interaction kernel(pseudo-potential) is systematically constructed by diagonalizing the Hamiltonian of the background field theory, by which the retardation effects are included in the interaction. Its wave function at the origin(WFO) behaves properly in a manner suggested by the covariant field theory. The equation can well be applied in the heavy quark effective theory.

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