Causality from dynamical symmetry: an example from local scale-invariance

Abstract

Physical ageing phenomena far from equilibrium naturally lead to dynamical scaling. It has been proposed to consider the consequences of an extension to a larger Lie algebra of local scale-transformation. The best-tested applications of this are explicitly computed co-variant two-point functions which have been compared to non-equilibrium response functions in a large variety of statistical mechanics models. It is shown that the extension of the Schrödinger Lie algebra $\mathfrak{sch}(1)$ to a maximal parabolic sub-algebra, when combined with a dualisation approach, is sufficient to derive the causality condition required for the interpretation of a two-point function as a physical response function. The proof is presented for the recent logarithmic extension of the differential operator representation of the Schrödinger algebra.

20 pages, Latex2e, 2 figures, final form (some references updated from v2)

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Cited by in corpus (9)

• Cyclic homology for Hom-associative algebras
• Ring Theoretic Aspects of Quandles
• Cohomology and Deformations of $n$-Lie algebra morphisms
• Non-local representations of the ageing algebra in higher dimensions
• Nonlinear reaction-diffusion systems with a non-constant diffusivity: conditional symmetries in no-go case
• Logarithmic Exotic Conformal Galilean Algebras
• Dynamical symmetries in the non-equilibrium dynamics of the directed spherical model
• Noncommutative products of Euclidean spaces
• Classification of simple weight modules over the 1-spatial ageing algebra