The phase space lattice differs fundamentally from the real space lattice because the two coordinates of phase space are noncommutative in quantum mechanics. As a result, a coherent state moving along a closed path in phase space acquires an additional phase factor, which is similar to the Aharonov–Bohm effect of a charged particle moving in a magnetic field. There is a deep connection between phase space and magnetic field. In fact, the canonical equation of motion can also be rewritten in the Lorenz-force form reflecting the symplectic geometry of classical phase space.