Abstract:
Scenarios for electroweak baryogenesis require an understanding of the effective potential at finite temperature near a first-order electroweak phase transition. Working in Landau gauge, we present a calculation of the dominant two-loop corrections to the ring-improved one-loop potential in the formal limit $g^4 \ll \lambda \ll g^2$, where $\lambda$ is the Higgs self-coupling and $g$ is the electroweak coupling. The limit $\lambda \ll g^2$ ensures that the phase transition is significantly first-order, and the limit $g^4 \ll \lambda$ allows us to use high-temperature expansions. We find corrections from 20 to 40\% at Higgs masses relevant to the bound computed for baryogenesis in the Minimal Standard Model. Though our numerical results seem to still rule out Minimal Standard Model baryogenesis, this conclusion is not airtight because the loop expansion is only marginal when corrections are as big as 40\%. We also discuss why super-daisy approximations do not correctly compute these corrections.

Abstract:
The effective potential of electroweak theory with two massless Higgs doublets at finite temperature is studied. We investigate phase structure and critical temperature in this model by numerical analysis without high-temperature expansion. The phase transition is found to be of first order. The critical temperature is shown to be relatively low for typical scalar masses. The free energy of the critical bubble is calculated with some approximations and we find that the bubble nucleation can occur at a temperature a little below the critical temperature. We also discuss the possibility of the electroweak baryogenesis.

Abstract:
The renormalization-group improved effective potential for an arbitrary renormalizable massless gauge theory in curved spacetime is found,thus generalizing Coleman-Weinberg's approach corresponding to flat space.Some explicit examples are considered,among of them:scalar self-interacting theory,scalar electrody namics,the asymptotically-free SU(2) gauge model,and the SU(5) GUT theory. The possibility of curvature-induced phase transitions is analyzed.It is shown that such a phase transition may take place in a SU(5) inflationary universe.The inclusion of quantum gravity effects isbriefly discussed.

Abstract:
The renormalization group (RG) is used in order to obtain the RG improved effective potential in curved spacetime. This potential is explicitly calculated for the Yukawa model and for scalar electrodynamics, i.e. theories with several (namely, more than one) mass scales, in a space of constant curvature. Using the $\lambda \varphi^4$-theory on a general curved spacetime as an example, we show how it is possible to find the RG improved effective Lagrangian in curved spacetime. As specific applications, we discuss the possibility of curvature induced phase transitions in the Yukawa model and the effective equations (back-reaction problem) for the $\lambda \varphi^4$-theory on a De Sitter background.

Abstract:
We compare two methods of analyzing the finite-temperature electroweak phase transition in the minimal supersymmetric standard model: the traditional effective potential (EP) approach, and the more recently advocated procedure of dimensional reduction (DR). The latter tries to avoid the infrared instabilities of the former by matching the full theory to an effective theory that has been studied on the lattice. We point out a limitation of DR that caused a large apparent disagreement with the effective potential results in our previous work. We also incorporate wave function renormalization into the EP, which is shown to decrease the strength of the phase transition. In the regions of parameter space where both methods are expected to be valid, they give similar results, except that the EP is significantly more restrictive than DR for the range of baryogenesis-allowed values of $\tan\beta$, $m_h$, the critical temperature, and the up-squark mass parameter $m_U$. In contrast, the DR results are consistent with $2\lsim\tan\beta\lsim 4$, $m_h<80$ GeV, and $m_U$ sufficiently large to have universality of the squark soft-breaking masses at the GUT scale, in a small region of parameter space. We suggest that the differences between DR and EP are due to higher-order perturbative corrections rather than infrared effects.

Abstract:
The renormalization-group improved effective potential ---to leading-log and in the linear curvature approximation--- is constructed for ``finite'' theories in curved spacetime. It is not trivial and displays a quite interesting, exponential-like structure ---in contrast with the case of flat spacetime where it coincides with the classical potential. Several possible cosmological applications, as curvature-induced phase transitions and modifications of the values of the gravitational and cosmological constants, are briefly discussed.

Abstract:
In a previous paper, the convergence of the effective field theory approach of Furnstahl, Serot and Tang to the nuclear many-body problem was studied by applying it to selected doubly-magic, and neighboring single-particle and single-hole, nuclei far from stability. The success of that approach, interpreted through density functional theory, would imply reliable densities. In this paper, the single-particle (Kohn-Sham) wave functions are probed using weak transitions near the Fermi surface. The weak currents are the Noether currents derived from the effective Lagrangian. The general single-particle transition matrix elements, from which any semi-leptonic weak rate can be calculated, are obtained in terms of upper and lower components of the Dirac wave functions. Here beta-decays in nuclei neighboring 132-Sn are studied and compared with available experimental data. Calibration of the theoretical results for such decays may also have useful application in element formation.

Abstract:
In collaboration with G.D. Moore, the electroweak phase transition in the minimal supersymmetric standard model is studied using the two-loop effective potential. We make a comprehensive search of the MSSM parameter space consistent with electroweak baryogenesis, taking into account various factors: the latest experimental constraints on the Higgs boson mass and the rho parameter, the possibility of significant squark and Higgs boson mixing, and the exact rate of bubble nucleation and sphaleron transitions. Most of the baryogenesis-allowed regions of parameter space will be probed by LEP 200, hence the Higgs boson is likely to be discovered soon if the baryon asymmetry was indeed created during the electroweak phase transition.

Abstract:
We investigate the quark backreaction on the Polyakov loop and its impact on the thermodynamics of quantum chromodynamics. The dynamics of the gluons generating the Polyakov-loop potential is altered by the presence of dynamical quarks. However, this backreaction of the quarks has not yet been taken into account in Polyakov-loop extended model studies. In the present work, we show within a 2+1 flavour Polyakov-quark-meson model that a quark-improved Polyakov-loop potential leads to a smoother transition between the low-temperature hadronic phase and the high-temperature quark-gluon plasma phase. In particular, we discuss the dependence of our results on the remaining uncertainties that are the critical temperature and the parametrisation of the Polyakov-loop potential as well as the mass of the sigma-meson.