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

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

2008-04-07

arxiv.org/abs/0804.1060v3

SIGMA 4:040,2008

Physics

High Energy Physics

High Energy Physics - Theory

This is a contribution to the Special Issue on Deformation Quantization, published in SIGMA (Symmetry, Integrability and Geome

Scientific paper

10.3842/SIGMA.2008.040

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 K\"ahler manifold, we prove that the Lie algebra of volume-preserving diffeomorphisms of the worldvolume can be approximated by $su(n)$, for $n\to\infty$. 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 $su(n)$.

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