On Field Theoretic Generalizations of a Poisson Algebra
Kanatchikov, I. V.
arXiv, 9710069 / Harvested from arXiv
Text on arXiv
A few generalizations of a Poisson algebra to field theory canonically formulated in terms of the polymomentum variables are discussed. A graded Poisson bracket on differential forms and an $(n+1)$-ary bracket on functions are considered. The Poisson bracket on differential forms gives rise to various generalizations of a Gerstenhaber algebra: the noncommutative (in the sense of Loday) and the higher-order (in the sense of the higher order graded Leibniz rule). The $(n+1)$-ary bracket fulfills the properties of the Nambu bracket including the ``fundamental identity'', thus leading to the Nambu-Poisson algebra. We point out that in the field theory context the Nambu bracket with a properly defined covariant analogue of Hamilton's function determines a joint evolution of several dynamical variables.
Publié le : 1997-10-08
Classification:  High Energy Physics - Theory,  General Relativity and Quantum Cosmology,  Mathematical Physics,  Mathematics - Differential Geometry,  Mathematics - Quantum Algebra 
@article{9710069,
     author = {Kanatchikov, I. V.},
     title = {On Field Theoretic Generalizations of a Poisson Algebra},
     journal = {arXiv},
     volume = {1997},
     number = {0},
     year = {1997},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9710069}
}

Kanatchikov, I. V. On Field Theoretic Generalizations of a Poisson Algebra. arXiv, Tome 1997 (1997) no. 0, . http://gdmltest.u-ga.fr/item/9710069/