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The Theory of Equivalent Lagrangians Revisited: A Symplectic Approach
Author(s) -
Rañada M. F.
Publication year - 1991
Publication title -
fortschritte der physik/progress of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.2190390106
Subject(s) - noether's theorem , symplectic geometry , lagrangian , hamiltonian (control theory) , mathematical physics , mathematics , hamiltonian system , hamiltonian lattice gauge theory , symplectomorphism , hamiltonian mechanics , covariant hamiltonian field theory , gauge theory , vector field , gauge symmetry , dynamical systems theory , pure mathematics , physics , quantum mechanics , geometry , phase space , mathematical optimization
The existence of different Lagrangian functions for the same dynamical vector field is studied using the methods of symplectic mechanics. The concept of Lagrangeoid transformation is introduced and its relation with the theory of bi‐Hamiltonian systems analyzed. The relation between equivalent (non‐gauge equivalent) Lagrangian formulations in TQ and their associated Hamiltonian dynamical systems in T * Q is developed and, finally, the Noether theorem is considered.