  We present a full microscopic theory based on the SU(2) covariant formulation
of the quasiclassical formalism to describe the Josephson current through an
extended superconductor-normal metal- superconductor (SNS) diffusive junction
with an intrinsic spin-orbit coupling (SOC) in the presence of a spin-splitting
field h. We demonstrate that the ground state of the junction corresponds to a
finite intrinsic phase difference 0 < {\phi}0 < 2{\pi} between the
superconductor electrodes provided that both, h and the SOC-induced SU(2)
Lorentz force are finite. In the particular case of a Rashba SOC we present
analytic and numerical results for {\phi}0 as a function of the strengths of
the spin fields, the length of the junction, the temperature and the properties
of SN interfaces.
