Nonrelativistic conformal transformations in Lagrangian formalism

TL;DR

This paper constructs nonrelativistic conformal transformations associated with N-Galilean conformal symmetries as point transformations in coordinate space, expanding the understanding of their geometric realization.

Contribution

It introduces a Lagrangian formalism for N-Galilean conformal symmetries, previously defined only in phase space, providing a new geometric perspective.

Findings

Conformal transformations are realized as point transformations in coordinate space.

The formalism extends the understanding of Galilean conformal symmetries.

Provides a Lagrangian approach to nonrelativistic conformal transformations.

Abstract

The conformal transformations corresponding to $N$-Galilean conformal symmetries, previously defined as canonical symmetry transformations on phase space, are constructed as point transformations in coordinate space.