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

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

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

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

Signatures of gravitational fixed points at the LHC

We study quantum-gravitational signatures at the CERN Large Hadron Collider (LHC) in the context of theories with extra spatial dimensions and a low fundamental Planck scale in the TeV range. Implications of a gravitational fixed point at high energies are worked out using Wilson¿s renormalization group. We find that relevant cross sections involving virtual gravitons become finite. Based on gravitational lepton pair production we conclude that the LHC is sensitive to a fundamental Planck scale of up to 6 TeV

Photon Self-Energy in a Color Superconductor

In a color superconductor the diquark condensates break spontaneously both the color and ordinary electromagnetism, leaving a remanining rotated U(1) symmetry unbroken. The gauge interactions associated to this rotated symmetry may be considered as the in-medium electromagnetism. We compute the in-medium photon self-energy in the presence of diquark condensates at high baryonic density and weak coupling. This is done to one-loop order for the cases of two and three quark flavors. For vanishing temperature, a detailed discussion is given of the low momentum behavior of the photon polarization tensor. A simple physical picture for the propagation of light in color superconducting media is obtained. The main new effect is due to the diquark condensates, which lead to a strong dielectric constant of the medium. The magnetic permeability remains unchanged, because the primary condensates have vanishing spin and angular momentum. In the two flavor case, an additional contribution arises due to gapless quarks and electrons, which is responsible for Debye screening effects. We also discuss the low energy effective theory for the three flavor case in the presence of electromagnetic interactions.Comment: 26 pages, 4 postscript figures, appendix added, to appear in PR

Effective Transport Equations for non-Abelian Plasmas

Starting from classical transport theory, we derive a set of covariant equations describing the dynamics of mean fields and their statistical fluctuations in a non-Abelian plasma in or out of equilibrium. A general procedure is detailed for integrating-out the fluctuations as to obtain the effective transport equations for the mean fields. In this manner, collision integrals for Boltzmann equations are obtained as correlators of fluctuations. The formalism is applied to a hot non-Abelian plasma close to equilibrium. We integrate-out explicitly the fluctuations with typical momenta of the Debye mass, and obtain the collision integral in a leading logarithmic approximation. We also identify a source for stochastic noise. The resulting dynamical equations are of the Boltzmann-Langevin type. While our approach is based on classical physics, we also give the necessary generalizations to study the quantum plasmas. Ultimately, the dynamical equations for soft and ultra-soft fields change only in the value for the Debye mass.Comment: 37 pages, revtex, no figures, section VII G modified, typos remove

Traditional roof coverings in the North York Moors National Park

Purpose – The paper seeks to deal with vernacular roofing practices within the North York Moors National Park. Design/methodology/approach – Initially the paper carries out a literature review of the geography and geology of the area and identifies what makes it physically unique. The paper then examines the development of various roofing materials, including thatch, stone slates and pantiles with case studies of old practice and modern methods from around the Park. Findings – Roofing styles are simplistic and have steered away from the intricate in favour of the indigenous or readily available. The paper demonstrates the much-regionalised nature of the roofing materials and recognises this as one of the special cultural features worthy of conservation. Research limitations/implications – The results are limited to the North York Moors National Park but the approach taken could be extended to other conservation areas. Practical implications – The results of the research will benefit those involved in the conservation of vernacular buildings in the North York Moors National Park. Originality/value – The paper calls for additional guidance for roofers and specifiers on traditional vernacular techniques and for existing funding under the Environmental Stewardship Scheme to be extended to include rural communities in National Parks

Deriving effective transport equations for non-Abelian plasmas

Within classical transport theory, an approach is presented to derive systematically effective collision terms and noise sources for effective kinetic equations of non-Abelian plasmas. This procedure amounts to the `integrating-out' of fluctuations, and is applicable for in- and out-of-equilibrium situations. When applied to a hot non-Abelian plasma close to equilibrium we recover the collision integral and the noise source first obtained by B\"odeker. It is also shown that our approach, and hence B\"odeker's effective theory, is consistent with the fluctuation-dissipation theorem.Comment: 7 pages, needs sprocl.sty, invited talk given by DFL at 5th workshop on QCD (QCD2000), Villefranche-sur-Mer, France, 3-7 Jan 200