Understanding the physical systems from their underlying geometrical and topological properties

• Published in: Physics of particles and nuclei letters Vol. 13; no. 1; pp. 26 - 31
• Main Author: Cirilo-Lombardo, Diego Julio
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 2016
• Subjects: Particle and Nuclear Physics; Physics; Physics and Astronomy; Physics of Elementary Particles and Atomic Nuclei. Theory; Dirac Equation; Nucleus Letter; Quantum Hall Effect; Topological Insulator; Coherent State
• ISSN: 1547-4771; 1531-8567
• DOI: 10.1134/S154747711601009X

As it is well known, a certain lack of theoretical understanding of the mechanisms governing the various phenomena exists in several areas of physics. In particular, it concerns those which involve transport of charged particles in low dimensions. In this work the physics of the 2-dimensional charge transport with parallel (in plane) magnetic field is analyzed from the geometrical and algebraic viewpoint making emphasis of how the physical interpretation arises from a consistent mathematical formulation of the problem. As a new result of this investigation with respect to the current literature we explicitly show that: (i) the specific form of the low dimensional Dirac equation enforces the field solution to fulfil the Majorana condition, (ii) the quantum Hall effect is successfully explained, (iii) a new topological effect (as the described by the Aharonov–Casher theorems) is presented and (iv) the link with supersymmetrical models is briefly commented.