The algebra of the energy-momentum tensor and the Noether currents in classical non-linear sigma models
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The recently derived current algebra of classical non-linear sigma models on arbitrary Riemannian manifolds is extended to include the energy-momentum tensor. It is found that in two dimensions the energy-momentum tensor θμυ, the Noether currentjμ associated with the global symmetry of the theory and the composite fieldj appearing as the coefficient of the Schwinger term in the current algebra, together with the derivatives ofjμ andj, generate a closed algebra. The subalgebra generated by the light-cone components of the energy-momentum tensor consists of two commuting copies of the Virasoro algebra, with central chargec=0, reflecting the classical conformal invariance of the theory, but the current algebra part and the semidirect product structure are quite different from the usual Kac-Moody/Sugawara type construction.
KeywordsNeural Network Manifold Complex System Nonlinear Dynamics Riemannian Manifold
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