Analytical Calculation of the Nucleation Rate for First Order Phase Transitions beyond the Thin Wall Approximation

First order phase transitions in general proceed via nucleation of bubbles. A theoretical basis for the calculation of the nucleation rate is given by the homogeneous nucleation theory of Langer and its field theoretical version of Callan and Coleman. We have calculated the nucleation rate beyond the thin wall approximation by expanding the bubble solution and the fluctuation determinant in powers of the asymmetry parameter. The result is expressed in terms of physical model parameters.Comment: 24 pages, 4 Postscript figures, LaTeX2

Chiral perturbation theory for three-flavour lattice QCD with isospin splitting

An important tool for the analysis of results of numerical simulations of lattice QCD is chiral perturbation theory. In Wilson chiral perturbation theory the effects of the finite lattice spacing $a$ are taken into account. In recent years the effects of isospin splitting on the masses of hadrons have been investigated in Monte Carlo simulations. Correspondingly, in this article we derive the expansions of the masses of the pseudoscalar mesons in chiral perturbation theory at next-to-leading order for twisted mass lattice QCD with three light quark flavours, taking the mass difference between the up and down quarks into account. The results include terms up to orders $m_q^2$ in the quark masses, $\Delta m^2$ in the mass splitting between up- and down quarks, and $a^2$ in the lattice spacing, respectively.Comment: 12 pages, revised version, as publishe

Chiral perturbation theory for lattice QCD with a twisted mass term

Quantum Chromodynamics on a lattice with Wilson fermions and a chirally twisted mass term for two degenerate quark flavours is considered in the framework of chiral perturbation theory. The pion mass and decay constant are calculated in next-to-leading order including terms linear in the lattice spacing $a$.Comment: 5 pages, LaTeX2e, typos corrected, 2 references adde

Renormalization Group Analysis of Turbulent Hydrodynamics

Turbulent hydrodynamics is characterised by universal scaling properties of its structure functions. The basic framework for investigations of these functions has been set by Kolmogorov in 1941. His predictions for the scaling exponents, however, deviate from the numbers found in experiments and numerical simulations. It is a challenge for theoretical physics to derive these deviations on the basis of the Navier-Stokes equations. The renormalisation group is believed to be a very promising tool for the analysis of turbulent systems, but a derivation of the scaling properties of the structure functions has so far not been achieved. In this work, we recall the problems involved, present an approach in the framework of the exact renormalisation group to overcome them, and present first numerical results.Comment: 43 pages, revised version, to be published in Physics Research Internationa