Instant Two-Body Equation in Breit Frame

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Abstract
A quasipotential formalism for elastic scattering from relativistic bound states is based on applying an instant constraint to both initial and final states in the Breit frame. This formalism is advantageous for the analysis of electromagnetic interactions because current conservation and four momentum conservation are realized within a three-dimensional formalism. Wave functions are required in a frame where the total momentum is nonzero, which means that the usual partial wave analysis is inapplicable. In this work, the three-dimensional equation is solved numerically, taking into account the relevant symmetries. A dynamical boost of the interaction also is needed for the instant formalism, which in general requires that the boosted interaction be defined as the solution of a four-dimensional equation. For the case of a scalar separable interaction, this equation is solved and the Lorentz invariance of the three-dimensional formulation using the boosted interaction is verified. For more realistic interactions, a simple approximation is used to characterize the boost of the interaction.

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