In previous works [1, 2], the 2-dimensional charge transport with parallel (in plane) magnetic field was considered from the theoretical point of view showing explicitly that the specific form of the emergent equation enforces the respective field solution to fulfil the Majorana condition. In this paper we review, explain and analyze these important results in the context of the generated physical effects, namely, the quantum ring as spin filter, the quantum Hall effect and a new one of pure topological origin (as the described by the Aharonov–Casher theorems). The link with supersymmetrical models is briefly discussed.

Charge dynamics, Majorana condition and the topology of the interacting electromagnetic field

It is generally believed that Majorana’s paper [4] describes particles which have no antiparticles. A thorough analysis have shown that this paper gives rise to the questions the answers to which have not been realized up to now. By the Majorana equation we mean the equation that describes stable, massive, and neutral leptons. Fulfillment of these three requirements leads strictly and unambiguously to the conclusion that the Majorana equation describes a pair of stable, massive, and neutral leptons, a particle and an antiparticle. This is similar to the Dirac equation, but the spin properties of the leptons of this type differ from the spin properties of the electron or positron.

/pdf/structure-of-the-majorana-s-equation-and-its-physical-4j2mp2d84l.pdf

Structure of the Majorana's equation and its physical interpretation

A sequence of necessary actions for the formulation of free leptonic equations (Dirac algorithm) is established. A complete and closed set of equations for the description of massive and massless, charged and neutral, stable and unstable leptons is obtained within a unified algorithmic approach. The Lorentz invariance and covariance of the newly derived equations is as rigorous as for the Dirac equation. All the established facts together explain the exceptional role of the structure of lepton equations that serves as a carrier of the properties of the observed particles.

Holistic Description of the Lepton Sector

Theory of matter under extreme conditions opens a new stage in particle physics. It is necessary here to combine Dirac's elementary particle physics with Prigogine's dynamics of nonequilibrium systems. In the article we discuss the problem of the hierarchy of complexity. What can be considered as the lowest level of the organization of extreme matter on the basis of which the self-organization of the complex form occur?

From lepton protoplasm to the genesis of hadrons

This article presents some arguments in favor of the necessity and opportunity to describe leptons and quarks on the united relativistic basis. The necessity is caused by experimental results of the relativistic nuclear physics. The opportunity has become really attainable taking into account the structure of the lepton equation groups and all their substructures obtained during the latest years.

/pdf/notes-on-the-problems-of-relativistic-nuclear-physics-30iehe5i2l.pdf

Notes on the problems of relativistic nuclear physics

Here I discuss a possibility to connect quantum numbers of elementary particles with their structure on the base of four connected components of Lorentz group. The complete and closed (with respect to homogenous Lorentz group) series of equations for description of lepton sector forms the pattern and ground for the present project.

The simplest and universal constituents for description of leptons and hadrons

We show that in some cases intrinsic symmetries are peculiar conversion or reflection of external symmetries. They form the structure of the microparticles and then determine interactions of these particles.

Notes on the nature of so-called intrinsic symmetries

A holistic study of the lepton sector is fulfilled in the framework of rigorous restrictions by five input suppositions. All leptons are divided into three classes on the structure of their equations. They are singlets, doublets and quartets. The quartet states are the most interesting among them from the point of view of their properties and possible physical interpretations.

Quartet states of the lepton sector

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The simplest and universal constituents for description of leptons and hadrons

Notes on the nature of so-called intrinsic symmetries

Quartet states of the lepton sector