Symmetries in Classical Field Theory
M. de Leon, D. Martin de Diego, A. Santamaria-Merino
TL;DR
This paper revisits the multisymplectic approach to Classical Field Theories, clarifying its relation with presymplectic formalism, and provides a comprehensive classification of symmetries and associated conservation laws.
Contribution
It offers a unified scheme for classifying infinitesimal symmetries in Classical Field Theories using multisymplectic and presymplectic formalisms.
Findings
Complete classification of infinitesimal symmetries
Derivation of conservation laws from symmetries
Clarification of the relation between multisymplectic and presymplectic formalisms
Abstract
The multisymplectic description of Classical Field Theories is revisited, including its relation with the presymplectic formalism on the space of Cauchy data. Both descriptions allow us to give a complete scheme of classification of infinitesimal symmetries, and to obtain the corresponding conservation laws.
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