Symmetry behavior in the Einstein universe: Gaussian approximation in the Schrödinger picture

Abstract

The effective potential for a scalar theory in the static Einstein universe is calculated using the Gaussian approximation in a field-theoretic Schrödinger picture. There occurs an infrared divergence in the slope of the effective potential at the would-be symmetry-breaking minimum and the effective potential is complex in a region including this would-be minimum. Spontaneous symmetry breaking, therefore, cannot occur in the static Einstein universe. © 1988 The American Physical Society.