A RELATIVISTIC QUANTUM EQUATION FOR N-GREATER-THAN-OR-EQUAL-TO-2 BOSONS IN 2 SPACE-TIME DIMENSIONS

We give a quantum and relativistic eigenvalue equation for N greater-than-or-equal-to 2 bosons in two space-time dimensions, which generalizes the corresponding Schrodinger equation. More precisely we find three self-adjoint operators P (momentum), H (Hamiltonian) and L (generator of the Lorentz transformations), acting on the Hilbert space of N free bosons in the Schrodinger picture, which satisfy the commutation rules of the Poincare algebra. The eigenvalue equation for the mass operator M2 = H2 - P2 leads to the above mentioned N-body equation. The possible existence of an eigenvalue assures that this model is non trivial.