Inverse Variational Problem and Symmetry in Action: The Relativistic Third Order Dynamics
General Mathematics
2017-08-22 v2
Abstract
Tools of the intrinsic analysis on manifolds, helpful in solving the invariant inverse problem of the calculus of variations are being presented comprising a combined approach which consists in the simultaneous imposition of symmetry principles and the inverse variational problem considerations in terms of vector-valued differential forms. In three-dimensional space-time we obtain a unique (covector) third-order Poincar\'e-invariant variational equation, which then is identified with the motion of a free relativistic top in flat three-dimensional space-time.
Keywords
Cite
@article{arxiv.1608.03197,
title = {Inverse Variational Problem and Symmetry in Action: The Relativistic Third Order Dynamics},
author = {Roman Ya. Matsyuk},
journal= {arXiv preprint arXiv:1608.03197},
year = {2017}
}
Comments
Corrected formulae on pp. 10 and 15. arXiv admin note: substantial text overlap with arXiv:1604.08451. Corrected formulae in V2:(3.9); (3.31); first of Proposition 3.6