New instantons in the double - well potential

A new instanton solution is found in the quantum-mechanical double-well potential with a four-fermion term. The solution has finite action, S = −m3 3λ − ( mA 4 √ 2λ + g 261m 8960 ) ǫξiξjξkξl, where A is a bosonic collective coordinate, 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.