Local scale invariance, conformal invariance and dynamical scaling

TL;DR

This paper develops local scale invariance concepts related to conformal invariance, identifying two types of local scale transformations that serve as dynamical symmetries in certain non-local field theories, with applications to Lifshitz points and ferromagnet ageing.

Contribution

It introduces two novel types of local scale invariance compatible with dynamical scaling, expanding the symmetry framework for non-local field theories.

Findings

Identifies two types of local scale invariance as dynamical symmetries.

Applies the framework to uniaxial Lifshitz points.

Explores implications for ageing in ferromagnets.

Abstract

Building on an analogy with conformal invariance, local scale transformations consistent with dynamical scaling are constructed. Two types of local scale invariance are found which act as dynamical space-time symmetries of certain non-local free field theories. Physical applications include uniaxial Lifshitz points and ageing in simple ferromagnets.