Mathematical operation in quantum optics, general relativity and other areas of physics
In theoretical physics, the Bogoliubov transformation, also known as the Bogoliubov–Valatin transformation, was independently developed in 1958 by Nikolay Bogolyubov and John George Valatin for finding solutions of BCS theory in a homogeneous system.[1][2] 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 stationary solutions of the corresponding Schrödinger equation. The Bogoliubov transformation is also important for understanding the Unruh effect, Hawking radiation, Davies-Fulling radiation (moving mirror model), pairing effects in nuclear physics, and many other topics.
The Bogoliubov transformation is often used to diagonalize Hamiltonians, with a corresponding transformation of the state function. Operator eigenvalues calculated with the diagonalized Hamiltonian on the transformed state function thus are the same as before.
^Valatin, J. G. (March 1958). "Comments on the theory of superconductivity". Il Nuovo Cimento. 7 (6): 843–857. Bibcode:1958NCim....7..843V. doi:10.1007/bf02745589. S2CID 123486856.
^Bogoljubov, N. N. (March 1958). "On a new method in the theory of superconductivity". Il Nuovo Cimento. 7 (6): 794–805. Bibcode:1958NCim....7..794B. doi:10.1007/bf02745585. S2CID 120718745.
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