  In the first attempt to introduce gauge theories in physics, Hermann Weyl,
around the 1920s, proposed certain scale transformations to be a fundamental
symmetry of nature. Despite the intense use of Weyl symmetry that has been made
over the decades, in various theoretical settings, this idea never found its
way to the laboratory. Recently, building-up from work by Lochlainn
O'Raifeartaigh and collaborators on the Weyl-gauge symmetry, applications of
Weyl-symmetry to the electronic properties of graphene have been put forward,
first, in a theoretical setting, and later, in an experimental proposal. Here I
review those results, by enlarging and deepening the discussion of certain
aspects, and by pointing to the steps necessary to make graphene a testing
ground of fundamental ideas.
