Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: De Donder-Weyl Hamiltonian formalism of MacDowell-Mansouri gravity   We analyse the behaviour of the MacDowell-Mansouri action with internal
symmetry group $\mathrm{SO}(4,1)$ under the covariant Hamiltonian formulation.
The field equations, known in this formalism as the De Donder-Weyl equations,
are obtained by means of the graded Poisson-Gerstenhaber bracket structure
present within the covariant formulation. The decomposition of the internal
algebra $\mathfrak{so}(4,1)\simeq\mathfrak{so}(3,1)\oplus\mathbb{R}^{3,1}$
allows the symmetry breaking $\mathrm{SO}(4,1)\to\mathrm{SO}(3,1)$, which
reduces the original action to the Palatini action without the topological
term. We demonstrate that, in contrast to the Lagrangian approach, this
symmetry breaking can be performed indistinctly in the covariant Hamiltonian
formalism either before or after the variation of the De Donder-Weyl
Hamiltonian has been done, recovering Einstein's equations via the
Poisson-Gerstenhaber bracket.

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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: econ