Nonlinear Bogolyubov-Valatin transformations and quaternions

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dc.creatorvan Holten, J. -W.
dc.creatorScharnhorst, K.
dc.date2004-11-23
dc.date2005-10-20
dc.date.accessioned2026-07-07T11:32:54Z
dc.date.available2026-07-07T11:32:54Z
dc.descriptionIn 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.
dc.description6 pages REVTEX (v3: two paragraphs appended, minor stylistic changes, eq. (39) corrected, references [10]-[14], [36], [37], [41], [67]-[69] added; v4: few extensions, references [62], [63] added, final version to be published in J. Phys. A: Math. Gen.)
dc.identifierhttps://arxiv.org/abs/quant-ph/0411170
dc.identifierhttp://arxiv.org/abs/quant-ph/0411170
dc.identifierJ.Phys.A38:10245-10252,2005
dc.identifierdoi:10.1088/0305-4470/38/47/012
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/197758
dc.subjectQuantum Physics
dc.subjectStrongly Correlated Electrons
dc.subjectHigh Energy Physics - Phenomenology
dc.subjectMathematical Physics
dc.subjectNuclear Theory
dc.titleNonlinear Bogolyubov-Valatin transformations and quaternions
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