Using a functional formalism, we investigate the effect of radiative corrections on the possibility of spontaneous symmetry breaking. We find that in some models, in particular, massless gauge theories with scalar mesons, the radiative corrections can induce spontaneous symmetry breaking, even though the classical approximation indicates that the vacuum is symmetric. Among the consequences of this phenomenon is a relationship between the masses of the scalar and vector mesons, predicting (for small coupling constants) that the scalar mesons are much lighter. We also apply our analysis to models in which the classical approximation indicates an asymmetric vacuum, including one in which our methods are particularly useful because the classical approximation does not completely specify the nature of the vacuum. It is possible to improve our analysis by the use of renormalization group methods; we do this for several models.ii

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It is possible for a classical field theory to have two stable homogeneous ground states, only one of which is an absolute energy minimum. In the quantum version of the theory, the ground state of higher energy is a false vacuum, rendered unstable by barrier penetration. There exists a well-established semiclassical theory of the decay of such false vacuums. In this paper, we extend this theory to include the effects of gravitation. Contrary to naive expectation, these are not always negligible, and may sometimes be of critical importance, especially in the late stages of the decay process.