Coordinate noncommutativity as low energy effective dynamics

Abstract

Coordinate noncommutativity, rather than being introduced through deformations of operator products, is achieved by coupling an auxiliary system with large energy excitations to the one of interest. Integrating out the auxiliary dynamics, or equivalently taking ground state expectation values, leads to the desired coordinate noncommutativity. The product responsible for this noncommutativity is different from the Groenewold-Moyal one. For products of operators at unequal times, this procedure differs from the normal, commutative one, for time differences smaller than ones characterized by the auxiliary system; for larger times the operator algebra reverts to the usual one.