Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 4 (2008), 040, 10 pages      arXiv:0804.1060
Contribution to the Special Issue on Deformation Quantization

Quantum Dynamics on the Worldvolume from Classical su(n) Cohomology

José M. Isidro and Pedro Fernández de Córdoba
Grupo de Modelización Interdisciplinar Intertech, Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Valencia 46022, Spain

Received February 05, 2008, in final form March 28, 2008; Published online April 15, 2008

A key symmetry of classical p-branes is invariance under worldvolume diffeomorphisms. Under the assumption that the worldvolume, at fixed values of the time, is a compact, quantisable Kähler manifold, we prove that the Lie algebra of volume-preserving diffeomorphisms of the worldvolume can be approximated by su(n), for n → ∞. We also prove, under the same assumptions regarding the worldvolume at fixed time, that classical Nambu brackets on the worldvolume are quantised by the multibrackets corresponding to cocycles in the cohomology of the Lie algebra su(n).

Key words: branes; Nambu brackets; Lie-algebra cohomology.

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