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Article Dans Une Revue Journal of Statistical Mechanics: Theory and Experiment Année : 2019

Infinite-dimensional meta-conformal Lie algebras in one and two spatial dimensions

Malte Henkel
Stoimen Stoimenov
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Résumé

Meta-conformal transformations are constructed as sets of time-space transformations which are not angle-preserving but contain time- and space translations, time-space dilatations with dynamical exponent and whose Lie algebras contain conformal Lie algebras as sub-algebras. They act as dynamical symmetries of the linear transport equation in d spatial dimensions. For d  =  1 spatial dimensions, meta-conformal transformations constitute new representations of the conformal Lie algebras, while for their algebraic structure is different. Infinite-dimensional Lie algebras of meta-conformal transformations are explicitly constructed for d  =  1 and d  =  2 and they are shown to be isomorphic to the direct sum of either two or three centre-less Virasoro algebras, respectively. The form of co-variant two-point correlators is derived. An application to the directed Glauber–Ising chain with spatially long-ranged initial conditions is described.

Dates et versions

hal-01914498 , version 1 (06-11-2018)

Identifiants

Citer

Malte Henkel, Stoimen Stoimenov. Infinite-dimensional meta-conformal Lie algebras in one and two spatial dimensions. Journal of Statistical Mechanics: Theory and Experiment, 2019, 1908, pp.084009. ⟨10.1088/1742-5468/ab3282⟩. ⟨hal-01914498⟩
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