Convergence and stability of the renormalisation group

Within the exact renormalisation group approach, it is shown that stability properties of the flow are controlled by the choice for the regulator. Equally, the convergence of the flow is enhanced for specific optimised choices for the regularisation. As an illustration, we exemplify our reasoning for 3d scalar theories at criticality. Implications for other theories are discussed.Comment: 8 pages, 4 figures, uses ActaStyle.cls, invited talk given at RG2002, March 10-16, 2002, Strba, Slowaki

The Effects of Gravitational Slip on the Higher-Order Moments of the Matter Distribution

Cosmological departures from general relativity offer a possible explanation for the cosmic acceleration. To linear order, these departures (quantified by the model-independent parameter $\varpi$, referred to as a `gravitational slip') amplify or suppress the growth of structure in the universe relative to what we would expect to see from a general relativistic universe lately dominated by a cosmological constant. As structures collapse and become more dense, linear perturbation theory is an inadequate descriptor of their behavior, and one must extend calculations to non-linear order. If the effects of gravitational slip extend to these higher orders, we might expect to see a signature of $\varpi$ in the bispectrum of galaxies distributed on the sky. We solve the equations of motion for non-linear perturbations in the presence of gravitational slip and find that, while there is an effect on the bispectrum, it is too weak to be detected with present galaxy surveys. We also develop a formalism for incorporating scale dependence into our description of gravitational slip.Comment: 25 pages, 9 figure

Aspects of semi-classical transport theory for QCD

We discuss some aspects of a recently proposed semi-classical transport theory for QCD plasmas based on coloured point particles. This includes the derivation of effective transport equations for mean fields and fluctuations which relies on the Gibbs ensemble average. Correlators of fluctuations are interpreted as collision integrals for the effective Boltzmann equation. The approach yields a recipe to integrate-out fluctuations. Systematic approximations (first moment, second moment, polarisation approximation) based on a small plasma parameter are discussed as well. Finally, the application to a hot non-Abelian plasma close to thermal equilibrium is considered and the consistency with the fluctuation-dissipation theorem established.Comment: Presented at Strong and Electroweak Matter (SEWM2000), Marseille, France, 14-17 June 2000, 12 page

Transport theory and low energy properties of colour superconductors

The one-loop polarisation tensor and the propagation of ``in-medium'' photons of colour superconductors in the 2SC and CFL phase is discussed. For a study of thermal corrections to the low energy effective theory in the 2SC phase, a classical transport theory for fermionic quasiparticles is invoked.Comment: 5 pages, talk given at the International Conference on "Statistical QCD", Bielefeld, August 26-30, 200

Derivative expansion and renormalisation group flows

We study the convergence of the derivative expansion for flow equations. The convergence strongly depends on the choice for the infrared regularisation. Based on the structure of the flow, we explain why optimised regulators lead to better physical predictions. This is applied to O(N)-symmetric real scalar field theories in 3d, where critical exponents are computed for all N. In comparison to the sharp cut-off regulator, an optimised flow improves the leading order result up to 10%. An analogous reasoning is employed for a proper time renormalisation group. We compare our results with those obtained by other methods.Comment: 15 pages, 5 figure