Bo Söderberg
Teaching staff
High Precision Mean Field Results for Lattice Gauge Theories : with special attention paid to the gauge dependence of mean-field perturbation theory to finite order
Author
Summary, in English
We do mean-field perturbation theory for U(1) lattice gauge theory in the axial gauge, and evaluate corrections from fluctuations up to fourth order for the free energy and plaquette energy. Comparing with similar results previously obtained in the Feynman gauge we find, to those orders studied, a gauge dependence of the size of the first correction term neglected with one exception. This gauge dependence decreases rapidly as the order of the approximation is increased. To any finite order, results in axial gauge are better approximations than results in the Feynman gauge. We speculate why. Assuming it to be generally true, we evaluate the first correction beyond the one-loop mean-field approximation to the free energy of SU(2) gauge theory with Wilson action in the axial gauge. This correction brings the mean-field result very close to Monte Carlo results for β > 1.6. It also makes the mean-field result identical, within a narrow margin, to ressumed strong coupling results in the interval 1.6 < β < 2.4, thus showing the absence of a phase transition. For both groups studied, we find that the asymptotic series of mean-field perturbation theory give much better approximations than do ordinary weak coupling series.
Publishing year
1984
Language
English
Pages
171-188
Publication/Series
Nuclear Physics B
Volume
240
Issue
2
Document type
Journal article
Publisher
North-Holland
Topic
- Subatomic Physics
Status
Published
ISBN/ISSN/Other
- ISSN: 0550-3213