  Bloch theorem in ordinary quantum mechanics means the absence of the total
electric current in equilibrium. In the present paper we analyze the
possibility that this theorem remains valid within quantum field theory
relevant for the description of both high energy physics and condensed matter
physics phenomena. First of all, we prove that the total electric current in
equilibrium is the topological invariant for the gapped fermions that are
subject to periodical boundary conditions, i.e. it is robust to the smooth
modification of such systems. This property remains valid when the inter -
fermion interactions due to the exchange by bosonic excitations are taken into
account perturbatively. We give the proof of this statement to all orders in
perturbation theory. Thus we prove the weak version of the Bloch theorem, and
conclude that the total current remains zero in any system, which is obtained
by smooth modification of the one with the gapped charged fermions, periodical
boundary conditions, and vanishing total electric current. We analyse several
examples, in which the fermions are gapless. In some of them the total electric
current vanishes. At the same time we propose the counterexamples of the
equilibrium gapless systems, in which the total electric current is nonzero.
