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.
If the inline PDF is not rendering correctly, you can download the PDF file here.
1. Di Piazza A. Müller C. K. Hatsagortsyan Z. & Keitel C. H. (2012). Extremely high-intensity laser interactions with fundamental quantum systems. Rev. Mod. Phys. 84 1177.
2. Poder K. Tamburini M. Sarri G. Di Piazza A. Kuschel S. Baird C. D. & Zepf M. (2018). Experimental signatures of the quantum nature of radiation reaction in the field of an ultraintense laser Phys. Rev. X 8 031004.
3. Hegelich B. M. Labun L. & Labun O. Z. (2017) Finding quantum effects in strong classical potentials. J.Plasma Phys. 83(3) 595830301.
4. Pervushin V.N. & Skokov V.V. (2006). Kinetic description of fermion production in the oscillator representation Acta Physica Polonica B37(9) 2587–2600.
5. Pervushin V. N. Skokov V. V. Reichel A. V. Smolyansky S. A. & Prozorkevich A. V. (2005). The kinetic description of vacuum particle creation in the oscillator representation. International Journal of Modern Physics A 20(24) 5689–5704.
6. Friesen A.V. Prozorkevich A.V. Smolyansky S.A. & Bonitz M. (2007). Nonperturbative kinetics of electron-hole excitations in strong electric field. In Saratov Fall Meeting 2006: Laser Physics and Photonics Spectroscopy and Molecular Modeling VII eds. V.L. Derbov L.A. Melnikov and L.M. Babkov Proc. SPIE 6537 article id. 653707.
7. Smolyansky S.A. Bonitz M. & Tarakanov A.V. (2010). Strong field generalization of the interband transitions kinetics. Physics of Particles and Nuclei41(7) 1075–1078.
8. Smolyansky S. A. Panferov A. D. Blaschke D. B. Juchnowski L. K ̈ampfer B. & Otto A. (2017). Vacuum particle-antiparticle creation in strong fields as a field induced phase transition. Russ. Phys. J. 59(11) 1731–1738.
9. Panferov A. D. Smolyansky S. A. Titov A. I. Kaempfer B. Otto A. Blaschke D. B. & Juchnowski L. (2017). Field induced phase transition in the few photon regime EPJ Web Conf. 138 07004.
10. Dirac P. (1928). The quantum theory of the electron. Proc. R. Soc. Lond. A117 610–634.
11. Thomson M. (2013). Modern particle physics. Cambridge: Cambridge University Press.
12. Álvarez-Gaumé L. &Vázques-Mozo M. Á. (2012). An invitation to quantum field theory. Lecture Notes in Physics 839. Springer-Verlag Berlin Heidelberg. DOI:10.1007/978-3-642-23728-7_2