Quantum fluctuations of the quark condensate

The quantum fluctuations of the quark condensate are studied in a Nambu Jona-Lasinio model. Two Lorenz invariant regularizations are considered: a sharp 4-momentum cut-off and a soft gaussian regulator. The quantum fluctuations of the quark condensate are found to be large although chiral symmetry is not restored. Instabilities of the ground state appear when the system is probed by a source term proportional to the squared quark condensate. The instabilities are traced to unphysical poles introduced by the regulator and their effect is greatly enhanced when a sharp cut-off is used.