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

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.