More insights into symmetries in multisymplectic field theories
Abstract
This work provides a general overview for the treatment of symmetries in classical field theories and (pre)multisymplectic geometry. The geometric characteristics of the relation between how symmetries are interpreted in theoretical physics and in the geometric formulation of these theories are clarified. Finally, a general discussion is given on the structure of symmetries in the presence of constraints appearing in singular field theories. Symmetries of some typical theories in theoretical physics are analyzed through the construction of the relevant multimomentum maps which are the conserved quantities (by Noether's theorem) on the (pre)multisymplectic phase spaces.
Keywords
Cite
@article{arxiv.2301.01255,
title = {More insights into symmetries in multisymplectic field theories},
author = {Arnoldo Guerra and Narciso Román-Roy},
journal= {arXiv preprint arXiv:2301.01255},
year = {2023}
}
Comments
A Section of "Conclusions" is added. Some mathematical expressions on p. 23 are corrected. Other changes after "peer reviewing" have been made. New references are added. This paper reviews some of the content of previous works arXiv:1610.08689 [math-ph], 2107.08846 [math-ph], and 2210.07698 [math-ph], providing new contributions that expand the results of these references. 37 pages