EFFECTIVE POTENTIAL, VACUUM TUNNELLING AND THE 1-N EXPANSION

The problem of vacuum decay in quantum field theory, when the instability is the result of radiative corrections, is discussed. The large-N expansion of the O(N) quartic model in four (Euclideanized) dimensions is analysed in detail and it is shown that, although the effective potential has no lower bound, tunnelling solutions of the usual type (instantons) do not exist. This is shown to happen because that expansion of the action which begins with the effective potential is inappropriate for the kind of field configurations in question. The relevance of this result to the related problem in the Salam-Weinberg model is also discussed. © 1979.