Electronic Processes in Solid State: Dirac Framework

• Main Author: Klotins E.
• Format: Article
• Language: English
• Published: Sciendo 2019-02-01
• Series: Latvian Journal of Physics and Technical Sciences
• Subjects: canonical quantization; Dirac field; Hilbert spaces; quasi-particle birth/annihilation
• Online Access: http://www.degruyter.com/view/j/lpts.2019.56.issue-1/lpts-2019-0006/lpts-2019-0006.xml?format=INT

The present paper proposes canonical Dirac framework adapted for application to the electronic processes in solid state. The concern is a spatially periodic structure of atoms distinguished by birth and annihilation of particle states excited due to interaction with the electromagnetic field. This implies replacing the conventional energy-momentum relation specific of the canonical Dirac framework and permissible for particle physics by a case specific relation available for the solid state. The advancement is a unified and consistent mathematical framework incorporating the Hilbert space, the quantum field, and the special relativity. Essential details of the birth and annihilation of the particle states are given by an illustrative two-band model obeying basic laws of quantum mechanics, special relativity, and symmetry principles maintained from the canonical Dirac framework as a desirable property and as a prerogative for the study of the particle coupling and correlation.