Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1997-10-08
Rept.Math.Phys. 40 (1997) 225
Physics
High Energy Physics
High Energy Physics - Theory
10 pages, LaTeX2e. Missprint in Ref. 1 is corrected (hep-th/9709229 instead of ...029)
Scientific paper
10.1016/S0034-4877(97)85919-8
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.
No associations
LandOfFree
On Field Theoretic Generalizations of a Poisson Algebra does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On Field Theoretic Generalizations of a Poisson Algebra, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Field Theoretic Generalizations of a Poisson Algebra will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-130070