On M algebras, the quantization of Nambu mechanics, and volume preserving diffeomorphisms

Jan, 1996
16 pages
Published in:
  • Helv.Phys.Acta 70 (1997) 302-317
e-Print:
Report number:
  • ETH-TH-95-33

Citations per year

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Abstract:
M-branes are related to theories on function spaces A\cal{A} involving M-linear non-commutative maps from A××A\cal{A} \times \cdots \times \cal{A} to A\cal{A}. While the Lie-symmetry-algebra of volume preserving diffeomorphisms of T MT~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, [J1,,JM]=i[J_1,\cdots, J_M]=i\hbar. Concerning multidimensional integrability, an important generalisation of Lax-pairs is given.
  • field theory: scalar
  • membrane model: p-brane
  • Hamiltonian formalism
  • operator: algebra
  • symmetry breaking