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T: Fachverband Teilchenphysik
T 22: Quantenfeldtheorie II
T 22.5: Vortrag
Freitag, 7. März 2008, 15:00–15:15, KGI-HS 1016
Worldline approach to the Gross-Neveu model — •Klaus Klingmüller1, Gerald Dunne2, Holger Gies3, and Kurt Langfeld4 — 1Institut für Theoretische Physik E, RWTH Aachen, 52056 Aachen — 2Department of Physics, University of Connecticut, Storrs, CT 06269-3046, USA — 3Institut für Theoretische Physik, Universität Heidelberg, 69120 Heidelberg — 4School of Maths & Stats, University of Plymouth, Plymouth, PL4 8AA, England
The Gross-Neveu (GN) model is a simple fermionic theory mimicking aspects of QCD, but without gluons and a four-fermion interaction instead. For D = 2 dimensions, in the limit of an infinite number of fermion flavours, the phase diagram of the GN model is known exactly. Remarkably, it shows a crystalline phase with broken translational symmetry at large chemical potential and small temperature. An intriguing question is, if such phases exist for higher dimensional models and in particular in QCD. To compute fermionic determinants in these models we propose to apply worldline numerics. In this approach, the fermionic determinant is expressed in terms of a pathintegral of a pointlike particle which is then evaluated numerically with Monte Carlo techniques. As a first test, we re-derive various aspects of the analytically known phase diagram of the two dimensional GN model. We discuss the potential of our approach to be extended to higher dimensions.