Understanding the physical systems from their underlying geometrical and topological properties

DIEGO JULIO CIRILO

PHYSICS OF PARTICLES AND NUCLEI

MAIK NAUKA/INTERPERIODICA/SPRINGER

Año: 2016

1063-7796

As it is well known, a certain lack of theoretical understanding of the mechanisms governing thevarious phenomena exists in several areas of physics. In particular, it concerns those which involve transportof charged particles in low dimensions. In this work the physics of the 2dimensional charge transport withparallel (in plane) magnetic field is analyzed from the geometrical and algebraic viewpoint making emphasisof how the physical interpretation arises from a consistent mathematical formulation of the problem. As anew result of this investigation with respect to the current literature we explicitly show that: (i) the specificform 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 theAharonov?Casher theorems) is presented and (iv) the link with supersymmetrical models is briefly commented.