A hidden symmetry of conformally invariant Lagrangians

TL;DR

This paper reveals a hidden algebraic symmetry in conformally invariant Lagrangians, showing they are invariant not only under local dilatation gauge transformations but also to changes in the gauge connection, indicating insensitivity to measurement unit transport.

Contribution

It identifies a previously unnoticed algebraic symmetry in conformally invariant Lagrangians, extending their invariance beyond traditional conformal symmetry.

Findings

Conformally invariant Lagrangians are invariant to gauge connection changes.

This invariance implies insensitivity to measurement unit transport.

The symmetry is most evident in a metric independent, Palatini-like formulation.

Abstract

In this paper a hidden extra symmetry of conformally invariant Lagrangians occuring in physics is pointed out. This symmetry is most apparent in a metric independent, i.e. in a Palatini-like presentation of the variational problem. In such presentation, the usual conformal weight of fields can be encoded as local dilatation group gauge charges. The conventional conformal invariance of Lagrangians is then equivalent to dilatation gauge invariance. The claim of the paper is, that the most commonly occurring conformally invariant Lagrangians turning up in physics are not only invariant to local dilatation gauge transformations, but they are also invariant to any change of the dilatation gauge connection, meaning an additional algebraic symmetry property. In terms of dimensional analysis and differential geometry, this additional symmetry means complete insensitivity of the Lagrangian to the choice of the parallel transport rule of local measurement units throughout spacetime.