A new symmetry of the relativistic wave equation

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.

4 pages

References in corpus (2)

• Analogue Gravity
• On the Advancements of Conformal Transformations and their Associated Symmetries in Geometry and Theoretical Physics

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