Nonlinear Bogolyubov–Valatin transformations and quaternions
- 9 November 2005
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 38 (47) , 10245-10252
- https://doi.org/10.1088/0305-4470/38/47/012
Abstract
In introducing second quantization for fermions, Jordan and Wigner (1927/1928) observed that the algebra of a single pair of fermion creation and annihilation operators in quantum mechanics is closely related to the algebra of quaternions H. For the first time, here we exploit this fact to study nonlinear Bogolyubov-Valatin transformations (canonical transformations for fermions) for a single fermionic mode. By means of these transformations, a class of fermionic Hamiltonians in an external field is related to the standard Fermi oscillator.Keywords
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