arXiv subjects
Publications and source records attributed to Takeo Miura.
The eigenfunctions and eigenvalues of orbital angular momentum operator on noncommutative lattice for a circle poset by theta-quantization are constructed, and it is demonstrated that they are equivalent to those of the conventional quantum mechanics.
We show two independent theoretical methods which lead to generate eigen values of a composite two-particles system associated with the non-locality of EPR effect which was experimentally proved by Aspect and others.One method is to use the quantum groups (Woronowicz and Podles)and the other is to use the two-dimensional kappa-Poincare groups.The representation of Hilbert spaces of these groups has eigen functions and eigen values with real numbers on one dimensional spaces.The range of eigen values is real number,so that the composite two particles system in quantum groups can macroscopicly exists and it has a nonlocal effect.
In this paper we consider a connection between the Moyal formuration of quantum mechanics and noncommutative lattices on nonlocal spaces. The Moyal bracket generates SU(N) Lie algebras,and representations of these algebras correspond to Bratteli diagrams on Hilbert spaces of C*-algebras, and also representations of noncommutative lattices on nonlocal spaces correspond to the same diagrams. We will show that the quantization thus generates nonlocal spaces by the intermediation of Bratteli diagrams.The above connection are investigated in details in two definite cases, one is one-dimensional lattice QCD SU(N) fields on the unit circle, the other is Penrose lattice SU-type Lie algebra fields on the Penrose lattice.
Based on the technique of noncommutative geometry, it is shown that, by means of the concept of the theta quantization, there is an equivalence between the notion of the modular momentum of the Aharonov-Bohm effect and the notion of a noncommutative lattice over a circle poset.