Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-09-20
JHEP 0902:039,2009
Physics
High Energy Physics
High Energy Physics - Theory
44 pages, v2:typos corrected, references added
Scientific paper
10.1088/1126-6708/2009/02/039
We consider Nambu-Poisson 3-algebras on three dimensional manifolds $ {\cal M}_{3} $, such as the Euclidean 3-space $R^{3}$, the 3-sphere $S^{3}$ as well as the 3-torus $T^{3}$. We demonstrate that in the Clebsch-Monge gauge, the Lie algebra of volume preserving diffeomorphisms $SDiff({\cal M}_{3})$ is identical to the Nambu-Poisson algebra on ${\cal M}_{3}$. Moreover the fundamental identity for the Nambu 3-bracket is just the commutation relation of $ SDiff({\cal M}_{3})$. We propose a quantization prescription for the Nambu-Poisson algebra which provides us with the correct classical limit. As such it possesses all of the expected classical properties constituting, in effect, a concrete representation of Nambu-Lie 3-algebras.
Axenides Minos
Floratos Emmanuel
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