The Dirac equation for low dimensional systems

Author: irakli sikharulidze
Keywords: The Dirac equation, Low dimensional, Discrete transformations
Annotation:

The aim of the present work is to consider the peculiarities that arise when studying the Dirac equation for low dimensional systems. In the beginning general properties of the Dirac equation are reviewed with relation to continuous and discrete transformations. Afterwards, in connection to the study of continuous transformations, comes a brief review of the basic algebraic and topological structure of the Lorenz group, after which it is shown how the Dirac bispinor behaves under charge conjugation, space inversion and time reversal discrete transformations in the (3+1) dimensional Minkowski space. Then the same discrete transformations are considered in the (2+1) and (1+1) dimensional cases. In order to properly define these discrete transformations in the (2+1) dimensional case, a new degree of freedom is introduced.

Lecture files:

დირაკის განტოლება დაბალგანზომილებიანი სისტემებისათვის [ka]