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