Bound-state solutions, invariant scalar products, and conserved currents for a class of two-body relativistic systems

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Abstract
The simplest two-body relativistic system with direct interaction, described by two first-class constraints, is investigated. After a description of the multitime approach (canonical quantization without gauge fixings), the two coupled integro-differential wave equations are solved. The elementary solutions for the bound states are found and are shown to transform as irreducible representations of the Poincaré group. Invariant scalar products are introduced assuring the unitarity of the representations and some of the associated conserved currents are discussed. The initial data problem has been solved by means of a quantum canonical transformation, which transforms the integro-differential equations into differential equations.