Relativistic quantum mechanics for two interacting particles in one-time representation (Q1308493)

For two interacting particles no classical Hamiltonian mechanics consistent with the basic requirement of Poincaré invariance exists. \textit{P. Dirac} [``Lectures on quantum mechanics'', Yeshiva Univ., New York (1964)] has proposed a constraint technique which avoids this difficulty but uses different time variables for the two particles. By modifying a method proposed by \textit{L. Bel} and \textit{E. Ruiz} [J. Math. Phys. 29, No. 8, 1840-1846 (1988; Zbl 0652.46057)] the authors propose a model for the quantum system of two interacting particles that uses a Lorentz-invariant seven-dimensional hypersurface in the energy momentum space of the system. By assuming that the evolution of the quantum system in the energy-momentum representation will consist of functions defined on this hypersurface and then applying a Fourier-type transformation, the authors obtain the configuration space representation of the system which consists of functions depending on seven independent variables only, namely, time and two three-dimensional position vectors of the two particles.