An explicit realization of $\mathrm{U}\mathrm{}\left(n\right)\mathrm{}$ quantum holonomy is presented in the context of nonrelativistic (2 + 1)-dimensional electrodynamics and used to construct the adiabatic effective action. It is shown that the U(1) subgroup of the $\mathrm{U}\mathrm{}\left(n\right)\mathrm{}$ holonomy gives rise to an effective Chern-Simons topological mass term and its relationship with the fractional quantum Hall effect is discussed.

• Received 27 June 1986

DOI:https://doi.org/10.1103/PhysRevLett.57.1195