  We present the generalized quasiclassical theory of the long-range
superconducting proximity effect in heterostructures with strong ferromagnets,
where the exchange splitting is of the order of Fermi energy. In the
ferromagnet the propagation of spin-triplet Cooper pairs residing on the
spin-split Fermi surfaces is shown to be governed by the spin-dependent Abelian
gauge field which results either from the spin-orbital coupling or from the
magnetic texture. The additional gauge field enters into the quasiclassical
equations in superposition with the usual electromagnetic vector potential and
results in the generation of spontaneous superconducting currents and phase
shifts in various geometries which provide the sources of long-range
spin-triplet correlations. We derive the Usadel equations and boundary
conditions for the strong ferromagnet and consider several generic examples of
the Josephson systems supporting spontaneous currents.
