Series expansions for lattice Green functions

Details Series expansions for lattice Green functions Series expansions for lattice Green functions

2000-03-20

arxiv.org/abs/hep-lat/0003015v4

J.Phys.A33:5675-5692,2000

Physics

High Energy Physics

High Energy Physics - Lattice

18 pages, Latex. v2: Statement corrected in section 2. v3: A remark and 5 references added. v4: Four references added

Scientific paper

10.1088/0305-4470/33/32/306

Lattice Green functions appear in lattice gauge theories, in lattice models of statistical physics and in random walks. Here, space coordinates are treated as parameters and series expansions in the mass are obtained. The singular points in arbitrary dimensions are found. For odd dimensions these are branch points with half odd-integer exponents, while for even dimensions they are of the logarithmic type. The differential equations for one, two and three dimensions are derived, and the general form for arbitrary dimensions is indicated. Explicit series expressions are found in one and two dimensions. These series are hypergeometric functions. In three and higher dimensions the series are more complicated. Finally an algorithmic method by Vohwinkel, Luscher and Weisz is shown to generalize to arbitrary anisotropies and mass.

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