abstract

• We analyse the behaviour of the MacDowell-Mansouri action with internal symmetry group SO(4, 1) under the De Donder-Weyl 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 De Donder-Weyl formulation. The decomposition of the internal algebra so (4, 1) ≃ so(3, 1) O3,1 allows the symmetry breaking SO(4, 1) → 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 polysymplectic formalism either before or after the variation of the De Donder-Weyl Hamiltonian has been done, recovering Einsteins equations via the Poisson-Gerstenhaber bracket. © 2017 IOP Publishing Ltd Printed in the UK.

authors

• Berra Montiel Oscar Jasel
• Molgado Ramos Alberto
• Serrano-Blanco D.

publication date

• 2017-01-01

funding provided via

• CB-2014-243433  Grant

published in

• Classical and Quantum Gravity  Journal

keywords

• De Donder-Weyl equations; Einstein equat; gauge theory; gravity; Hamiltonian; Poisson-Gerstenhaber bracket; polysymplectic formalism

Digital Object Identifier (DOI)

• 10.1088/1361-6382/aa924a

start page

end page

volume

• 34

issue

• 23