  The Immirzi parameter is a constant appearing in the general relativity
action used as a starting point for the loop quantization of gravity. The
parameter is commonly believed not to show up in the equations of motion,
because it appears in front of a term in the action that vanishes on shell. We
show that in the presence of fermions, instead, the Immirzi term in the action
does not vanish on shell, and the Immirzi parameter does appear in the
equations of motion. It determines the coupling constant of a four-fermion
interaction. Therefore the Immirzi parameter leads to effects that are
observable in principle, even independently from nonperturbative quantum
gravity.
