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By introducing an unconventional realization of the Poincare algebra alt_1 ofspecial relativity as conformal transformations, we show how it may occur as adynamical symmetry algebra for ageing systems in non-equilibrium statisticalphysics and give some applications, such as the computation of two-timecorrelators. We also discuss infinite-dimensional extensions of alt_1 in thissetting. Finally, we construct canonical Appell systems, coherent states andLeibniz functions for alt_1 as a tool for bosonic quantization.Comment: Latex2e, 19 page

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