Instantons in four-Fermi term broken supersymmetric quantum mechanics with general potential

Abstract

We have shown here how to find an integral representation for the solution of the Euclidean equations of motion of a quantum mechanical point particle in a general potential and in the presence of a four-Fermi term. The classical action in this theory depends explicitly on a set of four fermionic collective coordinates. The corrections to the classical action due to the presence of fermions are of topological nature in the sense that they depend only on the values of the fields at the boundary points τ → ±∞. As an application, the quantum mechanical sine-Gordon model with a four-Fermi term is solved explicitly and the corrections to the classical action are computed.