NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2016, 7 (2), P. 332–339
Dirac operator coupled to bosons
A. A. Boitsev – ITMO University, Kronverkskiy, 49, St. Petersburg, 197101, Russia; email@example.com
H. Neidhardt – Weierstrass Institute for Applied Analysis and Stochastics, Mohrenststr. 39, D-10117, Berlin, Germany; firstname.lastname@example.org
I.Y. Popov – ITMO University, Kronverkskiy, 49, St. Petersburg, 197101, Russia; email@example.com
We consider a model of point-like interaction between electrons and bosons in a cavity. The electrons are relativistic and are described by a Dirac operator on a bounded interval while the bosons are treated by second quantization. The model fits into the extension theory of symmetric operators. Our main technical tool to handle the model is the so-called boundary triplet approach to extensions of symmetric operators. The approach allows explicit computation of the Weyl function.
Keywords: Dirac operator, bosons, operator extension, boundary triplet, second quantization.