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Local gauge symmetries which are spontaneously broken in flat spacetime are shown to be restored for large spacetime curvatures. The case of symmetry breaking due to radiative quantum corrections in gauge theories with elementary scalar fields is considered explicitly. In spacetimes with a positive Ricci curvature scalar R and a cosmological event horizon, the critical curvature R, is of O(m$) or O(mwz), depending on whether the theory is formulated with conformal or minimal scalar fields. In Ricci flat spacetimes with a conventional event horizon the symmetry is expected to be restored when the temperature of the Hawking thermal radiation is of O(mw). This phenomenon is described in detail, using functional integral methods and dimensional renormalization, for massless scalar electrodynamics in de-Sitter spacetime. For conformal scalars, the symmetry restoring phase transition is first order, the critical curvature being R, = 0.910 mH a. For minima1 scalars, an anomalous, curvature dependent mass counterterm is required. The phase transition in this case is second order, and occurs at R, = 83.57 mwa. Symmetry restoration at finite temperature in flat spacetime is considered in an appendix. The critical temperature at which a first-order phase transition occurs in the Weinberg-Salam mode1 is found to be Tc = 0.329 mw .
On One-Dimensional Integrable Quantum Systems with Infinitely Many Degrees of Freedom. S. N. M.
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case it is well known) but also for the XY-model. It signals the existence of distinct surface and bulk transitions for sufficiently large values of KJK,. For the Ising model the complete program can be carried out and the phase diagram for films of arbitrary thickness is constructed. For the doubl