Differential equations for the Majorana particle in $${3+1}$$ and  $${1+1}$$ dimensions

Vincenzo, Salvatore De

doi:10.1134/s0040577921120060

Cited by 3 publications

(2 citation statements)

References 18 publications

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“…Indeed, only in the Majorana representation can the solutions of the Dirac equation describing a 1D Dirac-Majorana particle be real valued, but in any other representation, the solutions of the Dirac equation describing this particle are complex valued. Certainly, all these solutions satisfy the Majorana condition [27].…”

Section: Characterizing a 1d Kfgm Particle A Preliminariesmentioning

confidence: 99%

On wave equations for the Majorana particle in (3+1) and (1+1) dimensions

Vincenzo

2021

Preprint

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In general, the relativistic wave equation considered to mathematically describe the so-called Majorana particle is the Dirac equation with a real Lorentz scalar potential plus the so-called Majorana condition. Certainly, depending on the representation that one uses, the resulting differential equation changes. It could be a real or a complex system of coupled equations, or it could even be a single complex equation for a single component of the entire wave function. Any of these equations or systems of equations could be referred to as a Majorana equation or Majorana system of equations because it can be used to describe the Majorana particle. For example, in the Weyl representation, in (3+1) dimensions, we can have two non-equivalent explicitly covariant complex first-order equations; in contrast, in (1+1) dimensions, we have a complex system of coupled equations. In any case, whichever equation or system of equations is used, the wave function that describes the Majorana particle in (3+1) or (1+1) dimensions is determined by four or two real quantities. The aim of this paper is to study and discuss all these issues from an algebraic point of view, highlighting the similarities and differences that arise between these equations in the cases of (3+1) and (1+1) dimensions in the Dirac, Weyl, and Majorana representations. Additionally, to reinforce this task, we rederive and use results that come from a procedure already introduced by Case to obtain a two-component Majorana equation in (3+1) dimensions. Likewise, we introduce for the first time a somewhat analogous procedure in (1+1) dimensions and then use the results we obtain.

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Section: Characterizing a 1d Kfgm Particle A Preliminariesmentioning

confidence: 99%

On wave equations for the Majorana particle in (3+1) and (1+1) dimensions

Vincenzo

2021

Preprint

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“…In this paper we refer to the Majorana representation of a wave equation as a 'Majorana equation.' See Pal [25] for a review of Majorana and Weyl fermions, and De Vincenzo [26,27] for examples of solutions of Majorana and Weyl wavefunctions.…”

Section: On the Analogy Between The Maxwell And Dirac Equationsmentioning

confidence: 99%

On the Majorana representation of the optical Dirac equation

Dennis

Tijssen

Morgan

2023

J. Phys. A: Math. Theor.

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We consider the representations of the optical Dirac equation, especially ones where the Hamiltonian is purely real-valued. This is equivalent, for Maxwell’s equations, to the Majorana representation of the massless Dirac (Weyl) equation. We draw analogies between the Dirac, chiral and Majorana representations of the Dirac and optical Dirac equations, and derive two new optical Majorana representations. Just as the Dirac and chiral representations are related to optical spin and helicity states, these Majorana representations of the optical Dirac equation are associated with the linear polarisation of light. This provides a means to compare electron and electromagnetic wave equations in the context of classical ﬁeld theory.

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Characterizing Klein–Fock–Gordon–Majorana Particles in (1 + 1) Dimensions

De Vincenzo

2024

Few-Body Syst

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Differential equations for the Majorana particle in $${3+1}$$ and $${1+1}$$ dimensions

Cited by 3 publications

References 18 publications

On wave equations for the Majorana particle in (3+1) and (1+1) dimensions

On wave equations for the Majorana particle in (3+1) and (1+1) dimensions

On the Majorana representation of the optical Dirac equation

Characterizing Klein–Fock–Gordon–Majorana Particles in (1 + 1) Dimensions

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