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This article is cited in 1 scientific paper (total in 1 paper)
Quantum Dynamics on the Worldvolume from Classical $\mathrm{su}(n)$ Cohomology
José M. Isidro, Pedro Fernández de Córdoba Grupo de Modelización Interdisciplinar Intertech, Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Valencia 46022, Spain
Abstract:
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 $\mathrm{su}(n)$, 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 $\mathrm{su}(n)$.
Keywords:
branes; Nambu brackets; Lie-algebra cohomology.
Received: February 5, 2008; in final form March 28, 2008; Published online April 15, 2008
Citation:
José M. Isidro, Pedro Fernández de Córdoba, “Quantum Dynamics on the Worldvolume from Classical $\mathrm{su}(n)$ Cohomology”, SIGMA, 4 (2008), 040, 10 pp.
Linking options:
https://www.mathnet.ru/eng/sigma293 https://www.mathnet.ru/eng/sigma/v4/p40
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Abstract page: | 166 | Full-text PDF : | 43 | References: | 29 |
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