On Constrained-Instanton Valleys

We develop a systematic treatment for the quasi-zero modes, which play an important role in nonabelian gauge theories. It can be used to derive the analytic forms for the constrained instantons in the \ymh theory. This will automatically sum up contributions to all orders in $\rho$, the instanton size. We also give the analytic expressions for the instanton-antiinstanton pair, with an arbitrary relative phase. We apply the results to the computation for high energy baryon number violating cross section, as well as to Klinkhamer's new instanton.