On the Nature of the New Group LB1

The new local group LB1 introduced previously will be studied and reviewed in detail, depicting its unique nature that makes it a new group in fundamental physics. It will be made clear that even though most of its elements are Lorentz transformations, one unique discrete transformation not present in the Lorentz groups, is making this group into a new group because it is a reflection. In addition there will be four particular transformations onto the local light cone. It is these discrete transformations that allow for an isomorphism between the group U(1) and LB1. This result will have profound resonations in all of particle physics, general relativity, relativistic astrophysics, Riemannian geometry and group theory. These new group will be associated to a whole set of new experiments put forward.