The Schroedinger functional for Gross-Neveu models

Physics – High Energy Physics – High Energy Physics - Lattice

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

Ph.D. Thesis (Advisor: Dr. Rainer Sommer)

Scientific paper

Gross-Neveu type models with a finite number of fermion flavours are studied on a two-dimensional Euclidean space-time lattice. The models are asymptotically free and are invariant under a chiral symmetry. These similarities to QCD make them perfect benchmark systems for fermion actions used in large scale lattice QCD computations. The Schroedinger functional for the Gross-Neveu models is defined for both, Wilson and Ginsparg-Wilson fermions, and shown to be renormalisable in 1-loop lattice perturbation theory. In two dimensions four fermion interactions of the Gross-Neveu models have dimensionless coupling constants. The symmetry properties of the four fermion interaction terms and the relations among them are discussed. For Wilson fermions chiral symmetry is explicitly broken and additional terms must be included in the action. Chiral symmetry is restored up to cut-off effects by tuning the bare mass and one of the couplings. The critical mass and the symmetry restoring coupling are computed to second order in lattice perturbation theory. This result is used in the 1-loop computation of the renormalised couplings and the associated beta-functions. The renormalised couplings are defined in terms of suitable boundary-to-boundary correlation functions. In the computation the known first order coefficients of the beta-functions are reproduced. One of the couplings is found to have a vanishing beta-function. The calculation is repeated for the recently proposed Schroedinger functional with exact chiral symmetry, i.e. Ginsparg-Wilson fermions. The renormalisation pattern is found to be the same as in the Wilson case. Using the regularisation dependent finite part of the renormalised couplings, the ratio of the Lambda-parameters is computed.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

The Schroedinger functional for Gross-Neveu models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Schroedinger functional for Gross-Neveu models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Schroedinger functional for Gross-Neveu models will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-60177

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.