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-C quantum mechanics. A two dimensional representation of the new Dirac’s equation is therefore formulated and its solution is calculated.
Recently, the OPERA collaboration, according to their precision measurement, claims [
This paper is organized in the following manner. In the next section, the extended Lorentz transformation Model (ELTM), is presented and its application to neutrino is studied. In Section 3 application of ELTM to field theory is discussed. In Section 4 using the discovered dispersion relation a new Dirac’s equation (DE) within the framework of Generalized-C quantum mechanics (GCQM) is derived. Section 5 summarizes the results of the present investigation and also concluded remarks are given.
The basic idea of the proposed Extended Lorentz Transformation Model (ELTM) is the observation that the Minkowski metric