Bulg. J. Phys. vol.45 no.2 (2018), pp. 085-092

Bethe-Salpeter Equation with Massive Vector Particle Constituents

D.A. Owen
Ben-Gurion University of the Negev, Israel
Abstract. In the following article, it shall be demonstrated how the quantum field theory can be used to describe the two particle bound system, viz. by the Bethe-Salpeter equation. It is demonstrated that the formalism can be generalized to accommodate a bound state comprised of a scalar meson and a vector meson. The Bethe-Salpeter equation, in its original formulation was only able to accommodate a system of two fermions as it relied on the linearity of the momentum of the inverse propagators to obtain the equation with a perturbation expansion. This is crucial as there are no known exact solutions to this equation. It is shown that by introducing a two-component formalism, the inverse of both the scalar and vector meson propagators are linear in momentum and their bound state can be described adequately by the Bethe-Salpeter formalism.

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