Meta-Schr\"odinger invariance

TL;DR

This paper introduces the meta-Schr"odinger algebra as a symmetry in transport processes with ballistic and diffusive directions, extending it to an infinite-dimensional algebra and deriving related two-point functions.

Contribution

It constructs the meta-Schr"odinger algebra and its extension, providing new symmetry tools for non-stationary transport systems and their correlation functions.

Findings

Constructed the meta-Schr"odinger algebra and its Virasoro extension.

Derived covariant two-point functions for quasi-primary operators.

Proposed a generalized generator for non-stationary systems.

Abstract

The Meta-Schr\"odinger algebra arises as the dynamical symmetry in transport processes which are ballistic in a chosen `parallel' direction and diffusive and all other `transverse' directions. The time-space transformations of this Lie algebra and its infinite-dimensional extension, the meta-Schr\"odinger-Virasoro algebra, are constructed. We also find the representation suitable for non-stationary systems by proposing a generalised form of the generator of time-translations. Co-variant two-point functions of quasi-primary scaling operators are derived for both the stationary and the non-stationary cases.