Differential Forms in Electromagnetism: What are they good for?

by Prof. S. Kurz ((ETAS GmbH))

Thursday 2 Oct 2008, 11:00 → 12:00 Europe/Zurich

AB Auditorium Meyrin (CERN)

The calculus of differential forms has proven over the past decades to be an adequate and well-adapted tool for the formulation of the classical electromagnetic field theory. Advantages w.r.t. vector- or tensor-calculus are found, e.g., in the strict distinction between metric and topological concepts, as well as in the representation of fields and operators without any reference to coordinates. Moreover, the formalism is applicable for arbitrary dimension (e.g., 2-, 3-, 4-dimensional field problems), and arbitrary degrees of forms (e.g., scalar- vs. vector-potential formulation). It also lends itself in a natural way to discretization, since many object have discrete counterparts in the setting of algebraic topology.

In the further course of the talk a framework for dimensional reduction of field problems is presented that is based solely on differential forms on manifolds. It can be applied to problems of arbitrary dimension, degree of forms, and metric. As a consequence, 4-D field problems are reduced to two coupled and transient (3+1)-D field problems in exactly the same way a 3-D problem can be reduced to two coupled (2+1)-D problems. As an application, the Schiff Paradoxon is discussed, and compared to a 2-D formulation of a 3-D field problem with helical symmetry.

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