On the degrees of freedom of lattice electrodynamics

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.

arXiv comment14 pages, 6 figures

References in corpus (3)

• Unconditionally Stable Algorithms to Solve the Time-Dependent Maxwell Equations
• A geometric discretisation scheme applied to the Abelian Chern-Simons theory
• A doubled discretisation of abelian Chern-Simons theory

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