Symmetries of the semiclassical solutions of the vacuum tunneling problem

By investigating the cosmological consequences of the GUT's, one must compute the rate of generation of the bubbles characterized by a stable vacuum with broken internal symmetry in a background of a metastable vacuum with larger symmetry group. This is a kind of phase transition where the stable phase is dominated by the fluctuation around the global minima of the Higgs potential V(psi-vector). For the assumption that the original metastable phase occurs from the local minimum of V(psi-vector) at psi-vector=0, the tunneling probability per unit volume and unit time at the semiclassical level is well known. In previous papers related to this subject it was assumed that the geometrical symmetries of the minimizing solutions are maximal [i.e. O(4) or O(3)xT1] compatible with the boundary conditions. This paper gives an explicit proof of this conjecture for the multicomponent field