Smooth interpolation of lattice gauge fields by signal processing methods

Details Smooth interpolation of lattice gauge fields by signal processing methods Smooth interpolation of lattice gauge fields by signal processing methods

1995-09-29

arxiv.org/abs/hep-lat/9509094v1

Nucl.Phys.Proc.Suppl. 47 (1996) 823-826

Physics

High Energy Physics

High Energy Physics - Lattice

4 Pages, LaTex, Contribution to LATTICE 95, uses espcrc2.sty

Scientific paper

10.1016/0920-5632(96)00183-1

We digitally filter the Fourier modes of the link angles of an abelian lattice gauge field which produces the Fourier modes of a continuum $A_\mu(x)$ that exactly reproduces the lattice links through their definition as phases of finite parallel transport. The constructed interpolation is smooth ($C^\infty$), free from transition functions, and gauge equivariant. After discussing some properties of this interpolation, we discuss the non-abelian generalization of the method, arriving for SU(2), at a Cayley parametrization of the links in terms of the Fourier modes of $A^c_\mu(x)$. We then discuss the use of a maximum entropy type method to address gauge invariance in the non-abelian case.

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