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

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.

Latex2e, 19 pages

References in corpus (12)

• Non-relativistic conformal symmetries and Newton-Cartan structures
• Schr"odinger invariance and space-time symmetries
• Aging, rejuvenation and memory : the example of spin glasses
• Exotic Galilean Conformal Symmetry and its Dynamical Realisations
• Dynamics of glassy systems
• Acceleration-Extended Galilean Symmetries with Central Charges and their Dynamical Realizations
• Local scale-invariance and ageing in noisy systems
• Supersymmetric extensions of Schrödinger-invariance
• The exotic conformal Galilei algebra and nonlinear partial differential equations
• Dynamical symmetries of semi-linear Schrödinger and diffusion equations
• Local scale-invariances in the bosonic contact and pair-contact processes
• On non-local representations of the ageing algebra

Cited by in corpus (25)

• The BMS/GCA correspondence
• GCA in 2d
• Schrodinger Equations for Higher Order Non-relativistic Particles and N-Galilean Conformal Symmetry
• Supersymmetric Extension of Galilean Conformal Algebras
• Supersymmetric Extension of GCA in 2d
• The exotic conformal Galilei algebra and nonlinear partial differential equations
• Non-Relativistic Holography -- A Group-Theoretical Perspective
• Dynamical symmetries and causality in non-equilibrium phase transitions
• Logarithmic Correlators in Non-relativistic Conformal Field Theory
• Galilean contractions of $W$-algebras
• Metrics with Galilean Conformal Isometry
• On Holographic Realization of Logarithmic GCA
• Causality from dynamical symmetry: an example from local scale-invariance
• From conformal invariance towards dynamical symmetries of the collisionless Boltzmann equation
• Non-local meta-conformal invariance, diffusion-limited erosion and the XXZ chain
• Non-local representations of the ageing algebra in higher dimensions
• Logarithmic Exotic Conformal Galilean Algebras
• The derivations, central extensions and automorphism group of the Lie algebra $W$
• Logarithmic correlators or responses in non-relativistic analogues of conformal invariance
• Galilean conformal algebras in two spatial dimension
• Possible Central Extensions of Non-Relativistic Conformal Algebras in 1+1
• Higher-order Galilean contractions
• Multi-graded Galilean conformal algebras
• Aspects of infinite dimensional $\ell$-super Galilean conformal algebra
• Fractional Galilean Symmetries