Tensor product of quaternion hilbert modules

Aharon Razon*, L. P. Horwitz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


One of the main problems in the theory of quaternion quantum mechanics has been the construction of a tensor product of quaternion Hilbert modules. A solution to this problem is given by studying the tensor product of quaternion algebras (over the reals) and some of its quotient modules. Real, complex, and (covariant) quaternion scalar products are found in the tensor product spaces. Annihilationcreation operators are constructed, corresponding to the second quantization of the quaternion quantum theory with Bose-Einstein or Fermi-Dirac statistics. The gauge transformations of a tensor product vector and the gauge fields are studied.

Original languageEnglish
Pages (from-to)141-178
Number of pages38
JournalActa Applicandae Mathematicae
Issue number2
StatePublished - Aug 1991
Externally publishedYes


  • AMS subject classification (1991): 13C99, 16K20, 16Dxx, 46M05, 81Rxx, 81P99
  • Hilbert modules
  • Quaternions
  • algebraic modules
  • division algebras
  • ideals
  • non-Abelian gauge fields
  • tensor product


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