Downloads provided by UsageCountsNew multisymplectic approach to the Metric-Affine (Einstein-Palatini) action for gravity
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Gaset Rifà, Jordi; Román Roy, Narciso;
New multisymplectic approach to the Metric-Affine (Einstein-Palatini) action for gravity
We present a covariant multisymplectic formulation for the Einstein-Palatini (or Metric-Affine) model of General Relativity (without energy-matter sources). As it is described by a first-order affine Lagrangian (in the derivatives of the fields), it is singular and, hence, this is a gauge field theory with constraints. These constraints are obtained after applying a constraint algorithm to the field equations, both in the Lagrangian and the Hamiltonian formalisms. In order to do this, the covariant field equations must be written in a suitable geometrical way, using integrable distributions which are represented by multivector fields of a certain type. We obtain and explain the geometrical and physical meaning of the Lagrangian constraints and we construct the multimomentum (covariant) Hamiltonian formalism. The gauge symmetries of the model are discussed in both formalisms and, from them, the equivalence with the Einstein-Hilbert model is established.
Minor corrections. The bibliography has been updated. 36 pp
Spain
High Energy Physics - Theory, Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria, Field theory (Physics), Classificació AMS::55 Algebraic topology::55R Fiber spaces and bundles, Camps, Classificació AMS::53 Differential geometry::53D Symplectic geometry, :Matemàtiques i estadística::Matemàtica aplicada a les ciències [Àrees temàtiques de la UPC], FOS: Physical sciences, Geometria simplèctica, General Relativity and Quantum Cosmology (gr-qc), Classificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometry, General Relativity and Quantum Cosmology, contact geometry, jet bundles, metric-affine models, General relativity (Physics), :70 Mechanics of particles and systems::70S Classical field theories [Classificació AMS], :Matemàtiques i estadística::Geometria::Geometria computacional [Àrees temàtiques de la UPC], Camps, Teoria dels (Física), Classificació AMS::70 Mechanics of particles and systems::70S Classical field theories, Mathematical Physics, Einstein-Palatini action, Primary: 53D42, 55R10, 70S05, 83C05, Secondary: 49S05, 53C15, 53C80, 53Z05, Classical field theories, Classificació AMS::83 Relativity and gravitational theory::83C General relativity, multisymplectic forms, Symplectic geometry, Mathematical Physics (math-ph), Espais fibrats (Matemàtica), :53 Differential geometry::53D Symplectic geometry, contact geometry [Classificació AMS], :83 Relativity and gravitational theory::83C General relativity [Classificació AMS], :55 Algebraic topology::55R Fiber spaces and bundles [Classificació AMS], gauge symmetries, High Energy Physics - Theory (hep-th), Relativitat general (Física), Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències, Teoria dels (Física), Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria computacional, Fiber spaces (Mathematics), constraints, :Matemàtiques i estadística::Geometria [Àrees temàtiques de la UPC]
High Energy Physics - Theory, Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria, Field theory (Physics), Classificació AMS::55 Algebraic topology::55R Fiber spaces and bundles, Camps, Classificació AMS::53 Differential geometry::53D Symplectic geometry, :Matemàtiques i estadística::Matemàtica aplicada a les ciències [Àrees temàtiques de la UPC], FOS: Physical sciences, Geometria simplèctica, General Relativity and Quantum Cosmology (gr-qc), Classificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometry, General Relativity and Quantum Cosmology, contact geometry, jet bundles, metric-affine models, General relativity (Physics), :70 Mechanics of particles and systems::70S Classical field theories [Classificació AMS], :Matemàtiques i estadística::Geometria::Geometria computacional [Àrees temàtiques de la UPC], Camps, Teoria dels (Física), Classificació AMS::70 Mechanics of particles and systems::70S Classical field theories, Mathematical Physics, Einstein-Palatini action, Primary: 53D42, 55R10, 70S05, 83C05, Secondary: 49S05, 53C15, 53C80, 53Z05, Classical field theories, Classificació AMS::83 Relativity and gravitational theory::83C General relativity, multisymplectic forms, Symplectic geometry, Mathematical Physics (math-ph), Espais fibrats (Matemàtica), :53 Differential geometry::53D Symplectic geometry, contact geometry [Classificació AMS], :83 Relativity and gravitational theory::83C General relativity [Classificació AMS], :55 Algebraic topology::55R Fiber spaces and bundles [Classificació AMS], gauge symmetries, High Energy Physics - Theory (hep-th), Relativitat general (Física), Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències, Teoria dels (Física), Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria computacional, Fiber spaces (Mathematics), constraints, :Matemàtiques i estadística::Geometria [Àrees temàtiques de la UPC]
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