There has been much recent interest in the nature of the electroweak phase transition. This information is of importance in the context of the sphaleron models that have recently been proposed to explain the observed net baryon number in the Universe. The presence of a term that is cubic in the Higgs condensate in the one-loop effective potential appears to indicate a first-order phase transition. However, the infrared singularities inherent in massless models produce cubic terms that are of the same order in the coupling. In this paper, we include these terms and show that the standard model has a first-order phase transition. PACS number(s): 12.15.Ji, 05.70.Fh, 98.80.Cq

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The problem of maintaining gauge invariance when truncating the two particle irreducible (2PI) effective action has been studied recently by several authors. Here we give a simple and very general derivation of the gauge dependence identities for the off-shell 2PI effective action. We consider the case where the gauge is fixed by an arbitrary function of the quantum gauge field, subject only to the restriction that the Faddeev-Popov matrix is invertable. We also study the background field gauge. We address the role that these identies play in solving gauge invariance problems associated with physical quantities calculated using a truncated on-shell 2PI effective action. * Electronic address: carrington@brandonu.ca † Electronic address: g.kunstatter@uwinnipeg.ca ‡ Electronic address: zaraket@theory.uwinnipeg.ca

Plasmons of quark-gluon plasma, or gluon collective modes, are systematically studied. The plasma is, in general, nonequilibrium but homogeneous. We consider anisotropic momentum distributions of plasma constituents which are obtained from the isotropic one by stretching or squeezing in one direction. This leads to prolate or oblate distributions, respectively. We study all possible degrees of one-dimensional deformation from the extremely prolate case, when the momentum distribution is infinitely elongated in one direction to the extremely oblate distribution, which is infinitely squeezed in the same direction. In between these extremes we discuss arbitrarily prolate, weakly prolate, isotropic, weakly oblate, and arbitrarily oblate distributions. For each case, the number of modes is determined using a Nyquist analysis and the complete spectrum of plasmons is found analytically if possible and numerically when not. Unstable modes are shown to exist in all cases except that of isotropic plasma. We derive conditions on the wave vectors for the existence of these instabilities. We also discuss stable modes which are not limited to small domains of wave vectors and therefore have an important influence on the system's dynamics.