Instability of the translationally invariant vacuum of a system of fermions coupled to a chiral field

Abstract

It is shown, in the case of fermions coupled to a chiral field, that for every value of the coupling constant the energy of the B=0 sector is lower for a localized chiral field than for a translationally invariant (uniform) field. An expansion is given which converges for fields localized in a region of space smaller than the inverse mass of the fermions and which in lowest order explains the vacuum deformation. Exact energies are calculated for a hedgehog field. The instability of the uniform vacuum is found to increase with the winding number of the chiral field.