Cancellation of equilibrium parity-violating currents

It has recently been shown that in a rotating equilibrium system there exist neutrino and antineutrino currents parallel to the rotation axis. This suggests that particles other than neutrinos can also develop equilibrium currents if parity-violating weak interactions are taken into account. This possibility is examined using quantum field theory at finite temperature, density, and angular velocity. Regularization and renormalization of such a theory are discussed. The result obtained is negative. It is found that in the model considered the equilibrium current vanishes in the lowest order of perturbation theory. This is a surprising result, since the existence of a nonzero current is not forbidden by the symmetries of the Lagrangian. The question naturally arising from this result is whether a nonzero current appears in higher orders of perturbation theory or in different models or there is some deep physical reason which makes the equilibrium current equal to zero for all particles except neutrinos.