New instantons in the double well potential

Abstract

A new solution of the Euclidean equations of motion is found for the quantummechanical double-well potential with a four-fermion term. It extends the usual kinkinstanton solution in which both the kink field and the fermionic fields contain a finite number of new terms which are polynomial in the fermionic collective coordinates. The solution has finite action, S = −m3/3h + 9/140 mg eijklξiξjξkξl, where ξi, i = 1, ..., 4, are fermionic collective coordinates and g,m and λ are coupling constants. We explain why in general the instanton action can depend on collective coordinates.