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Since general relativity may be regarded as a non-Abelian gauge theory obtained by gauging the Lorentz group, one may obtain its q-deformation by gauging the q-Lorentz group. The q-dependent action resulting from this construction describes interacting gravitational and spinor fields. This action is invariant under nonlocal q-transformations. [ABSTRACT FROM AUTHOR]

Although there is no empirical motivation for replacing the commutators of dynamically conjugate operators in quantum mechanics by q-commutators, it appears possible to construct a consistent mathematical formulism based on this idea. To examine such a possibility further, we have studied the relation of this proposal to the Schwinger action principle, since the entire quantum mechanical formulism may be inferred from this principle. In particular, we have discussed the quantum transformation theory within this framework. [ABSTRACT FROM AUTHOR]