New instantons in the double-well potential

A new solution of the Euclidean equations of motion is found for the quantum-mechanical double-well potential with a four-fermion term. It extends the usual kink-instanton 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=−m33λ+9140 m g ϵijklξiξjξkξl, 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.