Bogoliubov transformation

In theoretical physics, the Bogoliubov transformation, also known as Bogoliubov-Valatin transformation, were independently developed in 1958 by Nikolay Bogolyubov and John George Valatin for finding solutions of BCS theory in a homogeneous system. The Bogoliubov transformation is an isomorphism of either the canonical commutation relation algebra or canonical anticommutation relation algebra. This induces an autoequivalence on the respective representations. The Bogoliubov transformation is often used to diagonalize Hamiltonians, which yields the steady-state solutions of the corresponding Schrödinger equation. The Bogoliubov transformation is also important for understanding the Unruh effect, Hawking radiation, pairing effects in nuclear physics, and many other topics.