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

TL;DR

This paper explores the Poincare algebra's role as a dynamical symmetry in ageing systems within non-equilibrium physics, introducing new representations, infinite-dimensional extensions, and tools like coherent states for quantization.

Contribution

It presents an unconventional realization of the Poincare algebra as conformal transformations and applies it to ageing systems, including the construction of Appell systems and coherent states.

Findings

Realization of Poincare algebra as conformal transformations in ageing systems

Development of infinite-dimensional extensions of the algebra

Construction of coherent states and Appell systems for quantization

Abstract

By introducing an unconventional realization of the Poincare algebra 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 alt_1 in this setting. Finally, we construct canonical Appell systems, coherent states and Leibniz functions for alt_1 as a tool for bosonic quantization.