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Physical Ageing and New Representations of Some Lie Algebras of Local Scale-Invariance

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Lie Theory and Its Applications in Physics

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 111))

Abstract

Indecomposable but reducible representations of several Lie algebras of local scale-transformations, including the Schrödinger and conformal Galilean algebras, and their applications in physical ageing are reviewed. The physical requirement of the decay of co-variant two-point functions for large distances is related to analyticity properties in the coordinates dual to the physical masses or rapidities.

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Notes

  1. 1.

    In the context of asymptotically flat 3D gravity, an isomorphic Lie algebra is known as BMS algebra, \(\mathfrak{b}\mathfrak{m}\mathfrak{s}_{3} \equiv \text{CGA}(1)\) [6–9].

  2. 2.

    The only previously known example of this had been obtained for the ageing algebra, where time-translations are excluded, see (24).

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Acknowledgements

M.H. is grateful to the organisers of LT-10 for the kind invitation. Ce travail a reçu du support financier par PHC Rila et par le Collège Doctoral franco-allemand Nancy-Leipzig-Coventry (Systèmes complexes à l’équilibre et hors équilibre) de l’UFA-DFH.

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  1. Groupe de physique Statistique, Institut Jean Lamour (CNRS UMR 7198), Université de Lorraine Nancy, B.P. 70239, F-54506, Vandœuvre-lès-Nancy Cedex, France

    Malte Henkel

  2. Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tsarigradsko Chaussee, Blvd., BG-1784, Sofia, Bulgaria

    Stoimen Stoimenov

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  1. Malte Henkel
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Correspondence to Malte Henkel .

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  1. Bulgarian Academy of Sciences, Institute for Nuclear Research and Nuclear Energy, Sofia, Bulgaria

    Vladimir Dobrev

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Henkel, M., Stoimenov, S. (2014). Physical Ageing and New Representations of Some Lie Algebras of Local Scale-Invariance. In: Dobrev, V. (eds) Lie Theory and Its Applications in Physics. Springer Proceedings in Mathematics & Statistics, vol 111. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55285-7_4

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