Theoretical Physics

Download PDF (455.6 KB) PP. 57 - 65 Pub. Date: June 1, 2019

DOI: 10.22606/tp.2019.42002

• Luca Nanni
  University of Ferrara, 44100-Ferrara, Italy

The infinite-component Majorana field is a promising tool for investigating phenomena that cannot yet be explained within the Standard Model framework, such as the oscillation of neutrino flavours, the origin of particle mass and the physical nature of dark matter. In this study, we demonstrated that the Lagrangian density of the fermionic Majorana field can be represented as the sum between the Dirac field with positive energy and the infinite Dirac-like tachyonic fields with negative frequency. Particularly, we demonstrated that the tachyonic components of the field are obtained by the superluminal Lorentz transformation (SLT) of the bradyonic components. Using this result, we obtained the explicit form of the SLT matrices, tachyonic creation and annihilation operators of the four-spinors on which they act. Thus, the Majorana field becomes the sum of the infinite Dirac fields transformed by the finite SLT matrices, which are a familiar tool in the physics of half-integer spin particles. A decay mechanism for an ordinary particle with tachyonic pair production is also proposed. The approach used in this study is an attempt to investigate particle physics beyond the Standard Model.

Infinite-dimensional matrices; Dirac field; superluminal Lorentz transformations; tachyon; tachyonic pair production.

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