On the degrees of freedom of lattice electrodynamics

Details On the degrees of freedom of lattice electrodynamics On the degrees of freedom of lattice electrodynamics

2004-08-04

arxiv.org/abs/hep-lat/0408005v2

Phys.Lett. A336 (2005) 1-7

Physics

High Energy Physics

High Energy Physics - Lattice

14 pages, 6 figures

Scientific paper

10.1016/j.physleta.2005.01.001

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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