Physical Coordinate as Eigen Values of Translation Operators in Non-commutative Spaces

TL;DR

This paper introduces two theoretical approaches using quantum groups and kappa-Poincare groups to derive eigenvalues related to the non-locality of the EPR effect, suggesting possible macroscopic quantum systems.

Contribution

It presents novel methods to generate eigenvalues for two-particle systems in non-commutative spaces, linking quantum group representations to nonlocal quantum phenomena.

Findings

Eigenvalues are real numbers, enabling macroscopic quantum systems.

The methods connect non-commutative geometry with quantum nonlocality.

Eigenfunctions exist within the representation spaces of the groups.

Abstract

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.