THE POINCARÉ ALGEBRA IN THE CONTEXT OF AGEING SYSTEMS: LIE STRUCTURE, REPRESENTATIONS, APPELL SYSTEMS AND COHERENT STATES

Confluentes Mathematici

STOIMENOV, STOIMEN¹  HENKEL, MALTE²  SCHOTT, RENɳ  UNTERBERGER, JÉRÉMIE⁴ 

[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;Institut Élie Cartan (IECN – CNRS UMR 7502), Université de Lorraine Nancy, B.P. 70239, F – 54506 Vandœuvre-lès-Nancy Cedex, France;Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, BG - 1784 Sofia, Bulgaria;LORIA (CNRS UMR 7503), Université de Lorraine Nancy, B.P. 70239, F – 54506 Vandœuvre-lès-Nancy Cedex, France

关键词: Poincaré algebra;    conformal Galilean algebra;    central extension;    non-equilibrium dynamical scaling;    Appell systems;   

DOI  :  10.1142/S1793744212500065

学科分类：数学（综合）

来源: World Scientific Publishing Co. Pte. Ltd.

【 摘 要 】

By introducing an unconventional realization of the Poincaré algebra $\mathfrak{alt}_1$ of special relativity as conformal transformations, we show how it may occur as a dynamical symmetry algebra for ageing systems in non-equilibrium statistical physics and give some applications, such as the computation of two-time correlators. We also discuss infinite-dimensional extensions of $\mathfrak{alt}_1$ in this setting. Finally, we construct canonical Appell systems, coherent states and Leibniz function for $\mathfrak{alt}_1$ as a tool for bosonic quantization.

【 授权许可】

Unknown