On MAlgebras, the Quantisation of NambuMechanics, and Volume Preserving Diffeomorphisms
Abstract
Mbranes are related to theories on function spaces $\cal{A}$ involving Mlinear noncommutative maps from $\cal{A} \times \cdots \times \cal{A}$ to $\cal{A}$. While the Liesymmetryalgebra of volume preserving diffeomorphisms of $T^M$ cannot be deformed when M>2, the arising Malgebras naturally relate to Nambu's generalisation of Hamiltonian mechanics, e.g. by providing a representation of the canonical Mcommutation relations, $[J_1,\cdots, J_M]=i\hbar$. Concerning multidimensional integrability, an important generalisation of Laxpairs is given.
 Publication:

arXiv eprints
 Pub Date:
 February 1996
 DOI:
 10.48550/arXiv.hepth/9602020
 arXiv:
 arXiv:hepth/9602020
 Bibcode:
 1996hep.th....2020H
 Keywords:

 High Energy Physics  Theory
 EPrint:
 16 pages, LaTex