Projection operators and states in the tensor product of quaternion hilbert modules
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.
AMS subject classifications (1991)13C99 16K20 16Dxx 46M05 81Rxx 81P99
KeywordsQuaternions algebraic modules division algebras tensor product non-Abelian gauge fields ideals Hilbert modules
Unable to display preview. Download preview PDF.
- 1.Piron C.: Foundations of Quantum Physics, Benjamin, New York, 1976, p. 75.Google Scholar
- 2.Gleason A. M.: J. Math. Mech. 6 (1957), 885.Google Scholar
- 3.Razon A. and Horwitz L. P.: Tensor product of quaternion Hilbert modules, Acta Appl. Math. 24 (1991), 141–178.Google Scholar
- 4.Nash C. G. and Joshi G. C.: J. Math. Phys. 28 (1987), 2883.Google Scholar