96-545 E. Frochaux

Relativistic quantum models for two bosons with interaction in the Schr\"{o}dinger picture (90K, LaTeX) Oct 30, 96

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Abstract. Relativistic quantum models are given, in the Schr\"{o}dinger picture, describing two bosons with interaction in four space-time dimensions. More precisely we start from the free model, involving functions $f(p_1,p_2)$ of two momenta $p_1, p_2 \in I\!\!R^3$ in the Hilbert space $L^2(I\!\!R^6,\sigma_2)$, where $\sigma_2$ is the Lorentz invariant measure. We add to the free Hamiltonian and the free Lorentz generators new interaction terms, such that the commutation rules of the Poincar\'{e} algebra remain satisfied. We get a large set of interaction terms solution to this problem. By integration we obtain unitary representations of the Poincar\'{e} group, in the same space $L^2(I\!\!R^6,\sigma_2)$. The existence of asymptotic states and of bound states assures that these models describe two particles with effective interaction.

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