Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric Representations of Whitney Forms and their Generalization to
  Minkowski Spacetime   In this work, we present two alternative yet equivalent representation
formulae for Whitney forms that are valid for any choice of coordinates, and
generalizes the original characterization of Whitney forms in Whitney (1957)
that requires the use of barycentric coordinates. In addition, we demonstrate
that these formulae appropriately generalize the notion of Whitney forms and
barycentric coordinates to Minkowski spacetime, and naturally to any other flat
pseudo-Riemannian manifold. These alternate forms are related to each other
through a duality between the exterior algebras on vectors and covectors. In
addition, these two formulae have a geometrically intuitive interpretation
which provide interesting insights into their structure. Furthermore, we obtain
an explicit characterization of the Hodge dual of the space of Whitney forms on
Minkowski spacetime, and this opens the door to treating the theory of
classical electromagnetism in a fully covariant fashion through the combination
of multisymplectic variational integration and spacetime finite-element
exterior calculus (FEEC) techniques. We conclude the paper with the results
from an $\mathbb{R}^{1+1}$ wave equation simulation, as a proof-of-concept of
the spacetime formulation described herein.

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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: cs
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The categories of this paper are: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph