Dynamical symmetries and causality in non-equilibrium phase transitions

TL;DR

This paper reviews the extension of dynamical symmetries, especially conformal invariance, to non-equilibrium phase transitions, emphasizing causality properties and their implications for response functions.

Contribution

It discusses recent developments in generalizing conformal invariance to non-equilibrium systems, focusing on causality and the scaling behaviour of space and time.

Findings

Generalization of conformal invariance to non-equilibrium phase transitions

Analysis of causality in covariant n-point functions

Implications for identifying responses and correlators

Abstract

Dynamical symmetries are of considerable importance in elucidating the complex behaviour of strongly interacting systems with many degrees of freedom. Paradigmatic examples are cooperative phenomena as they arise in phase transitions, where conformal invariance has led to enormous progress in equilibrium phase transitions, especially in two dimensions. Non-equilibrium phase transitions can arise in much larger portions of the parameter space than equilibrium phase transitions. The state of the art of recent attempts to generalise conformal invariance to a new generic symmetry, taking into account the different scaling behaviour of space and time, will be reviewed. Particular attention will be given to the causality properties as they follow for co-variant $n$-point functions. These are important for the physical identification of n-point functions as responses or correlators.