z-logo
Premium
Variational Equations and Symmetries in the Lagrangian Formalism; Arbitrary Vector Fields
Author(s) -
Grigore D. R.
Publication year - 1997
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.2190450803
Subject(s) - homogeneous space , lagrangian , mathematics , gauge symmetry , formalism (music) , abelian group , integrable system , helmholtz free energy , gauge theory , vector space , mathematical physics , classical mechanics , pure mathematics , physics , geometry , quantum mechanics , art , musical , visual arts
We continue the study of symmetries in the Lagrangian formalism of arbitrary order with the help of the generalized Helmholtz equations (sometimes called the Anderson‐Duchamp‐Krupka equations). For the case of second‐order equations and arbitrary vector fields we are able to establish a polynomial structure in the second‐order derivatives. This structure is based on the some linear combinations of Olver hyper‐Jacobians. We use as the main tools Fock space techniques and induction. This structure can be used to analyze Lagrangian systems with groups of Noetherian symmetries. As an illustration we analyze the case of Lagrangian equations with Abelian gauge invariance.

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here