A complete set of Feynman rules is derived, which permits a perturbative
description of the nonequilibrium dynamics of a symmetry-breaking phase
transition in λϕ4 theory in an expanding universe. In contrast to a
naive expansion in powers of the coupling constant, this approximation scheme
provides for (a) a description of the nonequilibrium state in terms of its own
finite-width quasiparticle excitations, thus correctly incorporating
dissipative effects in low-order calculations, and (b) the emergence from a
symmetric initial state of a final state exhibiting the properties of
spontaneous symmetry breaking, while maintaining the constraint ≡0. Earlier work on dissipative perturbation theory and spontaneous symmetry
breaking in Minkowski spacetime is reviewed. The central problem addressed is
the construction of a perturbative approximation scheme which treats the
initial symmetric state in terms of the field ϕ, while the state that
emerges at later times is treated in terms of a field ζ, linearly related
to ϕ2. The connection between early and late times involves an infinite
sequence of composite propagators. Explicit one-loop calculations are given of
the gap equations that determine quasiparticle masses and of the equation of
motion for and the renormalization of these equations is
described. The perturbation series needed to describe the symmetric and
broken-symmetry states are not equivalent, and this leads to ambiguities
intrinsic to any perturbative approach. These ambiguities are discussed in
detail and a systematic procedure for matching the two approximations is
described.Comment: 22 pages, using RevTeX. 6 figures. Submitted to Physical Review