STABILITY OR METASTABILITY AND EIGENVALUES OF THE EQUATION OF SMALL FLUCTUATIONS

Abstract

A theory with an asymmetric double-well potential is discussed and shown to possess a nontopological classical configuration like a bounce. It is then shown that the second variational derivative of the Euclidean action at this bounce-like configuration does not possess a negative eigenvalue. The significance of this observation is discussed in relation to more familiar models. Then a theory with a cubic potential is discussed and shown to possess a bounce with one negative eigenvalue of the second variational derivative which is indicative of metastability.