Classification of infinitesimal symmetries in covariant classical mechanics

Marco Modugno, Dirk Saller, and Jürgen Tolksdorf

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Submission date: 24. Jun. 2005
published in: Journal of mathematical physics, 47 (2006) 6, art-no. 062903 
DOI number (of the published article): 10.1063/1.2199068
Bibtex
MSC-Numbers: 17B26, 17B81, 37J05, 37J15, 58A20
Keywords and phrases: covariant classical mechanics, lie algebras and symmetries, jets, cosymplectic manifolds

Abstract:
In the framework of general relativistic classical mechanics on a spacetime with absolute time, we classify the infinitesimal symmetries of the classical structure by means of distinguished Lie subalgebras of the Lie algebra of ``special phase functions''.
These subalgebras are crucial also for the classification of infinitesimal quantum symmetries, which will be analysed in a forthcoming paper.