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 = -m(3)/3 lambda + 9/140 m g epsilon (ijkl) xi (i)xi (j)xi (k)xi (l), where xi (i), i = 1,...,4, are fermionic collective coordinates and g, m and lambda are coupling constants. We explain why in general the instanton action can depend on collective coordinates. (C) 2001 Published by Elsevier Science B.V.