A new Lagrangian dynamic reduction in field theory

DOI10.5802/aif.2549zbMath1404.58029arXiv1407.0263OpenAlexW1923136778MaRDI QIDQ983153

François Gay-Balmaz, Tudor S. Ratiu

Publication date: 3 August 2010

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.0263

zbMATH Keywords

Lagrangiancovariant reductionaffine Euler-Poincaré equationcovariant Euler-Poincaré equationdynamic reductionprincipal bundle field theory

Mathematics Subject Classification ID

Variational principles in infinite-dimensional spaces (58E30) Yang-Mills and other gauge theories in mechanics of particles and systems (70S15) Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems (70S05) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33) Lagrange's equations (70H03)

Related Items (18)

Lagrangian constraints and renormalization of 4D gravity ⋮ Clebsch variational principles in field theories and singular solutions of covariant EPDiff equations ⋮ Invariant variational problems on homogeneous spaces ⋮ Infinite-dimensional Lie groups and algebras in mathematical physics ⋮ Derivation of Hamilton-like equations on a non-Cauchy hypersurface and their expected connection to quantum gravity theories ⋮ Hamel's formalism for classical field theories ⋮ Foliation-based quantization and black hole information ⋮ Routh reduction for first-order Lagrangian field theories ⋮ Symmetry reduced dynamics of charged molecular strands ⋮ Lagrange-Poincaré field equations ⋮ Holographic quantization of gravity in a black hole background ⋮ Four-dimensional covariance of Feynman diagrams in Einstein gravity ⋮ Multisymplectic variational integrators and space/time symplecticity ⋮ Stochastic variational principles for dissipative equations with advected quantities ⋮ The Hamilton-Pontryagin principle and multi-Dirac structures for classical field theories ⋮ Reduction of gravity-matter and dS gravity to hypersurface ⋮ Cotangent bundle reduction and Routh reduction for polysymplectic manifolds ⋮ Dynamics of elastic strands with rolling contact

Cites Work

• Reduced Lagrangian and Hamiltonian formulations of Euler-Yang-Mills fluids
• The geometric structure of complex fluids
• Covariant and dynamical reduction for principal bundle field theories
• Reduction in principal bundles: covariant Lagrange-Poincaré equations
• Lagrangian reduction by stages
• Reduction in principal fiber bundles: Covariant Euler-Poincaré equations
• Euler-Poincaré reduction on principal bundles

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