The many body problem in relativistic quantum mechanics

Abstract

We discusse a relativistic Hamiltonian for an n-body problem in which all the masses are equal and all spins take value 1/2. In the frame of reference in which the total momentum $\check{P}=0$, the Foldy-Wouthuysen transformation is applies and the positive energy part of the Hamiltonian is separated. The Hamiltonian with unharmonic oscillator potential is applied to describe mass differences for charmonium and bottonium states.