On the Time-Like and Space-Like Components of Majorana Field

Abstract

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.

Majorana quanta, string scattering, curved spacetimes and the Riemann Hypothesis

“…In the Majorana solution one can build a set of exotic states through an infinite sum of four-spinor operators. In this way, the system can describe any interaction between different types of particle solutions resulting from the combination like a condensate of particles traveling slower, equal and faster than light (bradyons, tachyons and luxons), as described in [40,41], in a field consistent with the CPT invariance. This is in total agreement with the main properties of Majorana infinitecomponents quantum fields that include spin, mass distribution and tachyonic solutions [59][60][61] where the basic property of a Majorana particle is that a particle state, with its definite four-momentum and spin, can be transformed by a CPT transformation and a subsequent (space-time) Poincaré transformation into itself.…”

“…The modified Bessel function of the second kind K iν (x) of imaginary order iν for any fixed argument x > 0 possesses a countably infinite sequence of real zeros [38,39]. As the fixed argument m/a (j + 1/2) ∈ R this equation has zeros only if the term 1/2 + iE/2 is pure imaginary (as in decaying or scattering multi-particle processes described by the Majorana Tower [40,41]) and admits an infinite number of zeros, being isomorphic to a onedimensional Schrödinger equation with exponential potential. There is in fact a countably infinite number of (simple) real zeros in 1/2 + iE/2 once m/a (j + 1/2) > 0 is fixed for the equation K ν (X) = 0 where the variable is ν.…”

Majorana quanta, string scattering, curved spacetimes and the Riemann Hypothesis

“…A first example is the solution to the equation K iν (x) = 0, when the index is of imaginary order, iν, for any fixed argument x > 0 is characterized by a set of countably infinite sequence of real zeros [47,48]. In our case, the index ν is a complex number, ν = 1/2 + iE/2, and, with this method, this equation has zeros only if the term, e.g., 1/2 + iE/2 is pure imaginary (as it can occur in decaying or scattering processes involving multi-particle states described by the Majorana Tower [49,50]) and admits an infinite number of zeros, being isomorphic to a one-dimensional Schrödinger equation with exponential potential. In this particular case, there is in fact a countably infinite number of (simple) real zeros in 1/2 + iE/2 once m a j 1 2 0 ( )…”

“…In the Majorana solution one can build a set of exotic states through an infinite sum of four-spinor operators. In this way, the system can describe any interaction between different types of particle solutions resulting from the combination like a condensate of particles traveling slower, equal and faster than light (bradyons, tachyons and luxons), as described in [49,50], in a field consistent with the CPT invariance. This is in total agreement with the main properties of Majorana infinite-components quantum fields that include spin, mass distribution and tachyonic solutions [45,75,76] where the basic property of a Majorana particle is that a particle state, with its definite four-momentum and spin, can be transformed by a CPT transformation and a subsequent (space-time) Poincaré transformation into itself.…”