J.-W. van Holten, K. Scharnhorst: *Nonlinear Bogolyubov-Valatin
transformations and quaternions*.
Journal of Physics A: Mathematical and General **38**:47(2005)10245-10252
(DOI: 10.1088/0305-4470/38/47/012) [NIKHEF preprint NIKHEF 04-024, arXiv:quant-ph/0411170].
[INSPIRE record]

**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

- Electronic copy of the article: Journal of Physics A: Mathematical and General
- Electronic copy of the preprint: arXiv:quant-ph/0411170
- Citations
- Misprints, errata, addenda:

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