Spontaneously unbroken symmetry and gauge-invariant effective action

Abstract

It is shown how spontaneous symmetry breaking in gauge theories may be described by assigning vacuum expectation values only to gauge-invariant, renormalizable, composite operators. This description is primarily of use in analyzing the dynamics of symmetry-breaking phase transitions in the early universe. The abelian Higgs model is studied in detail. The theory is formulated most naturally in a unitary gauge, which is shown to be (essentially) renormalizable. The effective action is calculated in a gradient expansion. It is renormalizable, manifestly gauge invariant, and free from singularities which afflict the conventional effective potential. The extension to non-abelian theories is discussed, also in a unitary gauge. Although this gauge is generally not renormalizable, it is expected that finite results can be obtained for gauge-invariant quantities.