Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2005-01-25
Phys.Rev. D71 (2005) 054509
Physics
High Energy Physics
High Energy Physics - Lattice
9 pages, 11 figs., uses revtex4, modified presentation
Scientific paper
10.1103/PhysRevD.71.054509
We discuss the weak coupling expansion of a one plaquette SU(2) lattice gauge theory. We show that the conventional perturbative series for the partition function has a zero radius of convergence and is asymptotic. The average plaquette is discontinuous at g^2=0. However, the fact that SU(2) is compact provides a perturbative sum that converges toward the correct answer for positive g^2. This alternate methods amounts to introducing a specific coupling dependent field cut, that turns the coefficients into g-dependent quantities. Generalizing to an arbitrary field cut, we obtain a regular power series with a finite radius of convergence. At any order in the modified perturbative procedure, and for a given coupling, it is possible to find at least one (and sometimes two) values of the field cut that provide the exact answer. This optimal field cut can be determined approximately using the strong coupling expansion. This allows us to interpolate accurately between the weak and strong coupling regions. We discuss the extension of the method to lattice gauge theory on a D-dimensional cubic lattice.
Li Lexin
Meurice Yannick
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