A Realization of the infinite dimensional Symmetries of Conformal Mechanics

TL;DR

This paper explores how infinite-dimensional symmetries in conformal mechanics can be realized through time reparametrizations, extending known finite symmetries to a broader class using generalized transformation laws.

Contribution

It introduces a method to realize infinite-dimensional conformal symmetries as time reparametrizations by generalizing transformation laws for quasi-primary fields.

Findings

Infinite-dimensional symmetries can be realized as time reparametrizations.

A generalized transformation law for quasi-primary fields is developed.

The approach extends the SL(2,R) symmetry realization to infinite dimensions.

Abstract

We discuss the possibility of realizing the infinite dimensional symmetries of conformal mechanics as time reparametrizations, generalizing the realization of the SL(2,R) symmetry of the de Alfaro, Fubini, Furlan model in terms of quasi--primary fields. We find that this is possible using an appropriate generalization of the transformation law for the quasi-primary fields.