A geometrical meaning to the electron mass from breakdown of Lorentz invariance

Abstract

We discuss the problem of the electron mass in the framework of Deformed Special Relativity (DSR), a generalization of Special Relativity based on a deformed Minkowski space (i.e. a four-dimensional space-time with metric coefficients depending on the energy). We show that, by such a formalism, it is possible to derive the value of the electron mass from the space-time geometry via the experimental knowledge of the parameter of local Lorentz invariance breakdown, and of the Minkowskian threshold energy $E_{0,em}$ for the electromagnetic interaction. We put forward the suggestion that mass generation can be related, in DSR, to the possible dependence of mass on the metric background (relativity of mass).