A new symmetry of the relativistic wave equation

TL;DR

This paper uncovers a novel symmetry in the relativistic scalar wave equation related to metric redefinitions, which generalizes conformal transformations and introduces a new group structure affecting background geometry interpretation.

Contribution

It introduces a new symmetry in the relativistic wave equation involving metric redefinitions, expanding the understanding of geometric transformations in field theory.

Findings

Identifies a new symmetry related to metric redefinitions

Shows these transformations form a group structure

Highlights ambiguity in background geometry definition

Abstract

In this paper we show that there exists a new symmetry in the relativistic wave equation for a scalar field in arbitrary dimensions. This symmetry is related to redefinitions of the metric tensor which implement a map between non-equivalent manifolds. It is possible to interpret these transformations as a generalization of the conformal transformations. In addition, one can show that this set of manifolds together with the transformation connecting its metrics forms a group. As long as the scalar field dynamics is invariant under these transformations, there immediately appears an ambiguity concerning the definition of the underlying background geometry.