The renormalised quark mass in the Schrödinger functional of lattice QCD [Elektronische Ressource] : a one-loop calculation with a non-vanishing background field / von Stefan Kurth

The Renormalised Quark Mass in theSchr¨odinger Functional of Lattice QCDA One–Loop Calculation with a Non–Vanishing Background FieldD I S S E R T A T I O Nzur Erlangung des akademischen Gradesdoctor rerum naturalium(Dr. rer. nat.)im Fach Physikeingereicht an derMathematisch-Naturwissenschaftlichen Fakultat¨ Ider Humboldt-Universit¨at zu BerlinvonDipl.-Phys. Stefan Kurthgeboren am 10.04.1971 in BerlinPr¨asident der Humboldt-Universit¨at zu Berlin:Prof. Dr. J. MlynekDekan der Mathematisch-Naturwissenschaftlichen Fakult¨at I:Prof. Dr. M. LinscheidGutachter:1. Prof. Dr. Ulrich Wolff2. Prof. Dr. Michael Muller-Preußk¨ er3. Dr. Peter Weiszeingereicht am: 06.06.2002Tag der mundlic¨ hen Prufung:¨ 04.09.2002AbstractThe renormalised quark mass in the Schr¨odinger functional is studied perturba-tively with a non–vanishing background field.The framework in which the calculations are done is the Schr¨odinger func-tional. Its definition and basic properties are reviewed and it is shown how tomake the theory converge faster towards its continuum limit by O(a) improve-ment. It is explained how the Schr¨odinger functional scheme avoids the implica-tions of treating a large energy range on a single lattice in order to determine thescale dependence of renormalised quantities. The description of the scale depen-dencebythestepscalingfunctionisintroducedbothfortherenormalisedcouplingand the renormalised quark masses.