Projection operators and states in the tensor product of quaternion hilbert modules

Aharon Razon, L. P. Horwitz

Research output: Contribution to journalArticlepeer-review

Abstract

Following the construction of tensor product spaces of quaternion Hilbert modules in our previous paper, we define the analogue of a ray (in a complex quantum mechanics) and the corresponding projection operator, and through these the notion of a state and density operators. We find that there is a one-to-one correspondence between a state and an equivalence class of vectors from the tensor product space, which gives us another method to define the gauge transformations.

Original languageEnglish
Pages (from-to)179-194
Number of pages16
JournalActa Applicandae Mathematicae
Volume24
Issue number2
DOIs
StatePublished - Aug 1991
Externally publishedYes

Keywords

  • AMS subject classifications (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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