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On M-Algebras, the Quantisation of Nambu-Mechanics, and Volume Preserving Diffeomorphisms
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abstract
M-branes are related to theories on function spaces $\cal{A}$ involving M-linear non-commutative maps from $\cal{A} \times \cdots \times \cal{A}$ to $\cal{A}$. While the Lie-symmetry-algebra of volume preserving diffeomorphisms of $T^M$ cannot be deformed when M>2, the arising M-algebras naturally relate to Nambu's generalisation of Hamiltonian mechanics, e.g. by providing a representation of the canonical M-commutation relations, $[J_1,\cdots, J_M]=i\hbar$. Concerning multidimensional integrability, an important generalisation of Lax-pairs is given.
Forward citations
Cited by 1 Pith paper
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Towards Quantizing Null p-branes: Light-Cone Gauge Analysis and Physical Hilbert Space
Quantized null p-branes in light-cone gauge have physical Hilbert spaces split into p+1 classes of standing-wave states.
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