Nonlinear Bogolyubov-Valatin transformations and quaternions

J.W. van Holten; K. Scharnhorst

doi:10.1088/0305-4470/38/47/012

Nonlinear Bogolyubov-Valatin transformations and quaternions

J.W. van Holten, K. Scharnhorst

Physics and Astronomy

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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. © 2005 IOP Publishing Ltd.

Original language	English
Pages (from-to)	10245-10252
Journal	Journal of Physics A. Mathematical and General
Volume	38
Issue number	47
DOIs	https://doi.org/10.1088/0305-4470/38/47/012
Publication status	Published - 2005

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Nonlinear Bogolyubov-Valatin transformations and quaternions

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10.1088/0305-4470/38/47/012

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AB - 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. © 2005 IOP Publishing Ltd.

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DO - 10.1088/0305-4470/38/47/012

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JO - Journal of Physics A. Mathematical and General

JF - Journal of Physics A. Mathematical and General

IS - 47

ER -

Nonlinear Bogolyubov-Valatin transformations and quaternions

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