STABILITY OF GAUSSIAN APPROXIMATIONS IN MINISUPERSPACE - A VARIATIONAL APPROACH

Stability results are obtained for some special cases of finite-dimens ional approximations in minisuperspace field theory, using both rigoro us methods, based an theorems of the Kolmogorov-Arnold-Moser type, as well as perturbation theory. For a lambda phi(4) theory and a lower-di mensional truncation of the Hamiltonian it is shown that the evolution of coherent states in the homogeneous minisuperspace sector is indeed stable for positive values of the parameters that define the field th eory. It is also shown that for more realistic field-theoretical model s, however, Arnold diffusion could have destabilizing effects over ver y long times, The relevance of such a phenomenon requires consideratio n of each case separately.