Poisson–Poincaré reduction for field theories

Berbel, Miguel Á.; López, Marco Castrillón

doi:10.1016/j.geomphys.2023.104879

Cited by 3 publications

(1 citation statement)

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“…An alternative approach to Hamiltonian reduction that avoids the use of momentum maps consists of reducing the Poisson bracket [40]. This latter approach has been extended to covariant field theories yielding the Hamiltonian counterparts of the Euler-Poincaré and the Lagrange-Poincaré reduction theories, that is, the Lie-Poisson [11] and the Poisson-Poincaré [3] reduction theories, respectively. Of course, the Lagrangian and Hamiltonian viewpoints are related via the Legendre transform.…”

Section: Data Availability Statementmentioning

confidence: 99%

Gauge reduction in covariant field theory

Castrillón López,

Rodríguez Abella

2024

J. Phys. A: Math. Theor.

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In this work, we develop a Lagrangian reduction theory for covariant field theorieswith gauge symmetries. These symmetries are modeled by a Lie group fiber bundleacting fiberwisely on a configuration bundle. In order to reduce the variational principle,we utilize generalized principal connections, a type of Ehresmann connections that areequivariant by the fiberwise action. After obtaining the reduced equations, we give thereconstruction condition and we relate the vertical reduced equation with the Noethertheorem. Lastly, we illustrate the theory with several examples, including the classicalcase (Lagrange–Poincaré reduction), Electromagnetism, symmetry-breaking and non-Abelian gauge theories.

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Section: Data Availability Statementmentioning

confidence: 99%