The lattice Schwinger model as a discrete sum of filled Wilson loops

Details The lattice Schwinger model as a discrete sum of filled Wilson loops The lattice Schwinger model as a discrete sum of filled Wilson loops

1999-03-11

arxiv.org/abs/hep-lat/9903021v2

Nucl.Phys. B559 (1999) 539-562

Physics

High Energy Physics

High Energy Physics - Lattice

Revised version, to appear in Nucl. Phys. B. More technical details, Comment on chemical potential shortened, references added

Scientific paper

10.1016/S0550-3213(99)00467-8

Using techniques from hopping expansion we identically map the lattice Schwinger model with Wilson fermions to a model of oriented loops on the lattice. This is done by first computing the explicit form of the fermion determinant in the external field. Subsequent integration of the gauge fields renders a sum over all loop configurations with simple Gaussian weights depending on the number of plaquettes enclosed by the loops. In our new representation vacuum expectation values of local fermionic operators (scalars, vectors) can be computed by simply counting the loop flow through the sites (links) supporting the scalars (vectors). The strong coupling limit, possible applications of our methods to 4-D models and the introduction of a chemical potential are discussed.

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