Dirac equation and discrete symmetries in low dimensions

The central object of interest in the relativistic quantum theory – Dirac Equation has found a new applications in the studies of low dimensional condensed systems in the last 10-15 years. First of all, this applies to the new materials like graphene, where the spectrum of quasi-particles refer to massless Dirac particles in (2+1) dimensional space-time. Also Dirac Equation has an important part in the Jackiw-Rebbi models, which describe fermions interacting with solitonic fields and which is tied to the study of polyacetylene. Discrete symmetries, which are important characteristics of topological insulators, play an important role in the study of these fields. In this work we discuss properties discrete C, P, T symmetries of Dirac Equation in (2+1) and (1+1) dimensions. Also we will discuss discrete symmetries of the Dirac particle in the Kink type field.