  A Josephson junction made of a generic magnetic material sandwiched between
two conventional superconductors is studied in the ballistic semi-classic
limit. The spectrum of Andreev bound states is obtained from the
single-valuedness of a particle-hole spinor over closed orbits generated by
electron-hole reflections at the interfaces between superconducting and normal
materials. The semiclassical quantization condition is shown to depend only on
the angle mismatch between initial and final spin directions along such closed
trajectories. For the demonstration, an Andreev-Wilson loop in the composite
position/particle-hole/spin space is constructed, and shown to depend on only
two parameters, namely a magnetic phase shift and a local precession axis for
the spin. The details of the Andreev-Wilson loop can be extracted via measuring
the spin-resolved density of states. A Josephson junction can thus be viewed as
an analog computer of closed-path-ordered exponentials.
