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  • 1
    Electronic Resource
    Electronic Resource
    Tensor product of quaternion hilbert modules (1991)
    Springer
    Acta applicandae mathematicae 24 (1991), S. 141-178 
    Details
    ISSN: 1572-9036
    Keywords: 13C99 ; 16K20 ; 16Dxx ; 46M05 ; 81Rxx ; 81P99 ; Quaternions ; algebraic modules ; division algebras ; tensor product ; non-Abelian gauge fields ; ideals ; Hilbert modules
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00046890
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Projection operators and states in the tensor product of quaternion hilbert modules (1991)
    Springer
    Acta applicandae mathematicae 24 (1991), S. 179-194 
    Details
    ISSN: 1572-9036
    Keywords: 13C99 ; 16K20 ; 16Dxx ; 46M05 ; 81Rxx ; 81P99 ; Quaternions ; algebraic modules ; division algebras ; tensor product ; non-Abelian gauge fields ; ideals ; Hilbert modules
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00046891
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
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