Impossibility of maintaining local gauge symmetry on a lattice

Abstract

In a lattice system of non-abelian gauge field coupling to fermions, it is shown that a spontaneous breaking of local gauge symmetry is impossible (the Elitzur theorem) and it is argued further that a local gauge symmetry cannot be maintained in a lattice system of gauge field coupling to chiral fermions even if the chiral anomalies have been cancelled by adjusting fermion content. The physical implication of these results is briefly discussed.