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arXiv · hep-lat/0408005

On the degrees of freedom of lattice electrodynamics

Bo He·F. L. Teixeira
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Abstract

Using Euler's formula for a network of polygons for 2D case (or polyhedra for 3D case), we show that the number of dynamic\textit{\}degrees of freedom of the electric field equals the number of dynamic degrees of freedom of the magnetic field for electrodynamics formulated on a lattice. Instrumental to this identity is the use (at least implicitly) of a dual lattice and of a (spatial) geometric discretization scheme based on discrete differential forms. As a by-product, this analysis also unveils a physical interpretation for Euler's formula and a geometric interpretation for the Hodge decomposition.

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Bo He, F. L. Teixeira. 2005-01-03. On the degrees of freedom of lattice electrodynamics. https://doi.org/10.1016/j.physleta.2005.01.001

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