On the spin-orbit force in the Wilson loop context

Abstract

The Green function of the quark-antiquark system in the confining background field is analysed using the Feynman-Schwinger formalism. The Hamiltonian for the case of massive spinning quarks is obtained in the form containing essentially nonhermitian part. The eigenvalue problem for such type of the Hamiltonian is discussed, and it is shown that no complex eigenvalues arise. The corresponding no nunitary Foldy-Wouthuysen transformation is performed to obtain the hermitian Hamiltonian, and the standard spin-orbit interaction term is recovered.