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The breaking of global continuous symmetries in two-dimensional flat spacetime and in four-dimensional de Sitter spacetime is investigated. Infrared divergences require physically allowable quantum states in these spaces to break Lorentz or de Sitter invariance, resulting in two-point functions which are explicitly time dependent. Field expectation values which break the global symmetry must decay in time, but it is possible to have a state which exhibits broken symmetry for a finite time. It is also possible for field correlations and energy density produced by a broken-symmetry state to persist after the symmetry has been restored.
Ford et al. (1986) studied this question.