Twisted kink dynamics in multiflavor chiral Gross-Neveu model

Abstract

The Gross-Neveu model with ${\rm U}_L(N_f)\times{\rm U}_R(N_f)$ chiral symmetry is reconsidered in the large $N_c$ limit. The known analytical solution for the time dependent interaction of any number of twisted kinks and breathers is cast into a more revealing form. The ($x,t$)-dependent factors are isolated from constant coefficients and twist matrices. These latter generalize the twist phases of the single flavor model. The crucial tool is an identity for the inverse of a sum of two square matrices, derived from the known formula for the determinant of such a sum.