Bethe-Salpeter equation in Minkowski space with cross-ladder kernel

A new method for solving the Bethe-Salpeter equation is developed. It allows to find the Bethe-Salpeter amplitudes both in Minkowski and in Euclidean spaces and, as a by product, the light-front wave function. The method is valid for any kernel given by irreducible Feynman graphs. Bethe-Salpeter and Light-Front equations for scalar particles with ladder + cross-ladder kernel are solved.Comment: 7 pages, 5 figures, to appear in the proceedings of the Workshop on Light-Cone QCD and Nonperturbative Hadron Physics, Cairns, Australia, July 7-15, 200

Electromagnetic form factor via Minkowski and Euclidean Bethe-Salpeter amplitudes

The electromagnetic form factors calculated through Euclidean Bethe-Salpeter amplitude and through the light-front wave function are compared with the one found using the Bethe-Salpeter amplitude in Minkowski space. The form factor expressed through the Euclidean Bethe-Salpeter amplitude (both within and without static approximation) considerably differs from the Minkowski one, whereas form factor found in the light-front approach is almost indistinguishable from it.Comment: 3 pages, 2 figures. Contribution to the proceedings of the 20th International Conference on Few-Body Problems in Physics (FB20), Pisa, Italy, September 10-14, 2007. To be published in "Few-Body Systems

Light-Front Bethe-Salpeter Equation

A three-dimensional reduction of the two-particle Bethe-Salpeter equation is proposed. The proposed reduction is in the framework of light-front dynamics. It yields auxiliary quantities for the transition matrix and the bound state. The arising effective interaction can be perturbatively expanded according to the number of particles exchanged at a given light-front time. An example suggests that the convergence of the expansion is rapid. This result is particular for light-front dynamics. The covariant results of the Bethe-Salpeter equation can be recovered from the corresponding auxiliary three-dimensional ones. The technical procedure is developed for a two-boson case; the idea for an extension to fermions is given. The technical procedure appears quite practicable, possibly allowing one to go beyond the ladder approximation for the solution of the Bethe-Salpeter equation. The relation between the three-dimensional light-front reduction of the field-theoretic Bethe-Salpeter equation and a corresponding quantum-mechanical description is discussed.Comment: 42 pages, 5 figure

Study of relativistic bound states for scalar theories in Bethe-Salpeter and Dyson-Schwinger formalism

The Bethe-Salpeter equation for Wick-Cutkosky like models is solved in dressed ladder approximation. The bare vertex truncation of the Dyson-Schwinger equations for propagators is combined with the dressed ladder Bethe-Salpeter equation for the scalar S-wave bound state amplitudes. With the help of spectral representation the results are obtained directly in Minkowski space. We give a new analytic formula for the resulting equation simplifying the numerical treatment. The bare ladder approximation of Bethe-Salpeter equation is compared with the one with dressed ladder. The elastic electromagnetic form factors is calculated within the relativistic impulse approximation.Comment: 30 pages, 10 figures, accepted for publication in Phys. Rev.