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

Abstract

By introducing an unconventional realization of the Poincaré algebra <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi mathvariant="fraktur">alt</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> </mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi mathvariant="fraktur">alt</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> </mml:math> of in this setting. Finally, we construct canonical Appell systems, coherent states and Leibniz function for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi mathvariant="fraktur">alt</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> </mml:math> as a tool for bosonic quantization.