ANNUAL REPORT 2005 - Universiteit Utrecht

ANNUAL REPORT 20053 PhD programmeHenneman, A.A. (VUA)thesis title: Scale dependence of correlation on the light-frontadvisor: prof. dr. P.J.G. Muldersdate: 2 February 2005present position: research scientist, Department of Parasitology, Leiden UniversityMedical Center, the NetherlandsQuark distribution and fragmentation functions describe the probability of findinga quark with a specific polarization and fraction of the parent hadron’s momentum.These functions are being measured in highly energetic scattering experiments and aretreated in a field theoretic description. The field theory that describes the behaviourof quarks and gluons, the mediators of the force between quarks, is called QuantumChromodynamics (QCD). QCD posseses the property of asymptotic freedom, whichmeans that at high energy, quarks behave as if they were free and their interactionscan be described in pertubation theory. Consistent description of distribution andfragmentation functions within a QCD framework, requires to define these functionsincluding pertubative corrections. This results in functions depending on the scale,which can be regarded as a resolution, at which they are measured. This scale dependence,known as evolution, connects the nummerical values of these functions atthe different scales at which they were measured. In this thesis we present the resultsfor the scale dependence of a new type of distribution and fragmentation function,which appear when quark momentum in transverse directions with respect to thehighly energetic scattering is incorporated in the description. The evolution of thethese distribution and fragmentation functions has a complicated structure. This isnot suprising as inclusion of transverse quark momentum, leads to the presence ofadditional, quark-gluon interaction dependent functions in the evolution equations.Kadar, Z. (UU)thesis title: The polygon representation of three dimensional gravitation and its globalpropertiesadvisor: prof. dr. G. ’t Hooftco-advisor: dr. R. Lolldate: 18 April 2005present position: postdoctoral fellow, Mathematics Department, Heriot-Watt University,Edinburgh, UKThree dimensional Lorentzian general relativity with zero cosmological constant andspinless point particles is studied. The topology of spacetime is M x R, where Mis a Riemann surface and global hyperbolicity is assumed. The system has only afinite number of degrees of freedom corresponding to non-trivial topology, since allsolutions of the vacuum Einstein equations are locally flat spaces in three dimensions.After a generic introduction to phase space reduction, the polygon model of ’t Hooftis introduced.This finite dimensional Hamiltonian system is encoded in a number of Euclideanpolygons. It arises as the foliation of the three dimensional universe with spacelikeEucliden polygons, whose edges are decorated by two real numbers, their lengths L