New physics for superluminal particles

TL;DR

This paper proposes a theoretical framework extending Lorentz transformations and quantum mechanics to explain the superluminal neutrino speeds observed in the OPERA experiment, introducing new particles and equations.

Contribution

It introduces the Extended Lorentz Transformation Model and Generalized-$\\mathbb{C}$ quantum mechanics to account for superluminal particles and derives a new Dirac equation with solutions.

Findings

Development of a new Lorentz transformation model

Formulation of a generalized quantum mechanics

Derivation of a two-dimensional Dirac equation solution

Abstract

In this paper, we consider the apparent superluminal speed of neutrinos in their travel from CERN to Gran Susso, as measured by the OPERA experiment, within the framework of the Extended Lorentz Transformation Model. The model is based on a natural extension of Lorentz transformation by wick rotation. Scalar and Dirac's fields are considered and invariance under the new lorentz group is discussed. Moreover, an extension of quantum mechanics to accommodate new particles is considered using the newly proposed Generalized-$\mathbb{C}$ quantum mechanics. A two dimensional representation of the new Dirac's equation is therefore formulated and its solution is calculated.