Gauge Backgrounds from Commutators and the Role of Noncommutative Space

The gauge connections corresponding to electromagnetism, Yang-Mills theory and Einstein gravity can be derived by assuming specific commutation relations between the phase-space variables of a first quantized theory. Extending the procedure to noncommuting coordinates leads to new types of dynamics, which are explored. In particular, the conditions for the coexistence of an electromagnetic background and a noncommutative two-from are found, as well as a generalized mechanism of dimensional reduction. The noncommutative deformation of a gravitational background is also constructed. The present formulation suggests some simple experimental tests of noncommutativity.