Nonlinear Bogolyubov-Valatin transformations and quaternions

Details Nonlinear Bogolyubov-Valatin transformations and quaternions Nonlinear Bogolyubov-Valatin transformations and quaternions

2004-11-23

arxiv.org/abs/quant-ph/0411170v4

J.Phys.A38:10245-10252,2005

Physics

Quantum Physics

6 pages REVTEX (v3: two paragraphs appended, minor stylistic changes, eq. (39) corrected, references [10]-[14], [36], [37], [4

Scientific paper

10.1088/0305-4470/38/47/012

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.

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