Nonlinear Bogolyubov–Valatin transformations and quaternions

  title={Nonlinear Bogolyubov–Valatin transformations and quaternions},
  author={Jan Willem van Holten and Klaus Scharnhorst},
  journal={Journal of Physics A},
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… 
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