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arXiv · hep-lat/9509094

Smooth interpolation of lattice gauge fields by signal processing methods

James E. Hetrick
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Abstract

We digitally filter the Fourier modes of the link angles of an abelian lattice gauge field which produces the Fourier modes of a continuum $A_μ(x)$ 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 $A^c_μ(x)$. We then discuss the use of a maximum entropy type method to address gauge invariance in the non-abelian case.

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James E. Hetrick. 1995-09-29. Smooth interpolation of lattice gauge fields by signal processing methods. https://doi.org/10.1016/0920-5632(96)00183-1

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