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Parallel transfer is generalized to allow for the existence of a local gauge group. In spaces with torsion such a group may be introduced in a natural way and physically interpreted as a generalization of the electromagnetic gauge group. It is possible to construct simple theories of this type which correctly represent the isospin symmetries of the known fields. According to the program here proposed the local connection of microspace is restricted by the symmetries of the observed fields; the dynamics is then determined by the curvature of space, just as in the known macroscopic limit. In the models here considered the discrete groups are not discussed and all conservation laws are exact.

A generally covariant field theory, characterized by an asymmetric metric, an asymmetric connection, and an arbitrary gauge group is investigated as a possible formal basis for the experimentally observed strong couplings. Transposition invariance is put into correspondence with TCP invariance. The parts of the connection irreducible under both coordinate and gauge groups are identified with the independent boson fields. Representations of the strong and electromagnetic couplings of the baryon-meson system are found, subject to the same dynamical uncertainties as global and unitary symmetry. In the simplest version the pion and kaon fields correspond to the Hermitian torsion, while the vector bosons, including the photon, correspond to the anti-Hermitian torsion.