The Poincaré algebra in the context of ageing systems: Lie structure, representations, Appell systems and coherent states

Henkel, Malte; Schott, René; Stoimenov, Stoimen; Unterberger, Jérémie

Confluentes Mathematici, Tome 4 (2012) no. 4.

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 ${\mathfrak{alt}}_1$ of in this setting. Finally, we construct canonical Appell systems, coherent states and Leibniz function for ${\mathfrak{alt}}_1$ as a tool for bosonic quantization.

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