Classical and Quantum Theory with a New Symmetry

A formal symmetry between generalized coordinates and momenta is postulated to formulate classical and quantum theories of a particle coupled to an Abelian gauge field. It is shown that the symmetry (a) requires the field to have dynamic degrees of freedom and to be a connection in a non-flat space-time manifold, and (b) leads to a quantum theory free of the measurement problem. It is speculated that gravitomagnetism could be a possible source of the gauge field.