The effect of retardation on the spontaneous breaking of chiral symmetry in GCM

An effective Hamiltonian including current-current coupling from the global color symmetry model is derived. Retardation effects are introduced by the factor (R/root pi) e(-R2 tau2), instead of delta(tau) in the correlation k ernel, from which the retardation gap equation with alpha-alpha coupling in the P-3(0) vacuum is obtained. (q) over barq condensations of different re tardation parameters R with or without the alpha-alpha term are calculated. The results show the effects of retardation, and indicate that the typical value of R is about 2 fm(-1) at reasonable value of (q) over barq condensa tion. And while taking typical value 1 fm(-1) of R, the condensation [(q) o ver barq](1/3) is about 13% larger than that with no retardation effect. Wi th the alpha-alpha terms, the condensation [(q) over barq](1/3) is about 17 % larger than that without it for all values of the parameter R. This shows that the retardation effects and the alpha-alpha terms are important for f urther studying in the low-energy region.