Possible quantum kinematics. II. Non-minimal case

TL;DR

This paper develops noncommutative quantum analogs of Cayley-Klein spaces with various structures, introducing noncommutative constant curvature spaces and exploring their applications to quantum deformations of space-time models.

Contribution

It presents a comprehensive description of quantum Cayley-Klein spaces with non-minimal multipliers, expanding the framework for quantum kinematics and proposing new noncommutative space-time models.

Findings

Introduction of noncommutative analogs of constant curvature spaces.

Identification of quantum deformations applicable to realistic space-time models.

Development of a wide variety of quantum kinematics for theoretical physics.

Abstract

The quantum analogs of the N-dimensional Cayley-Klein spaces with different combinations of quantum and Cayley-Klein structures are described for non-minimal multipliers, which include the first and the second powers of contraction parameters in the transformation of deformation parameter. The noncommutative analogs of (N-1)-dimensional constant curvature spaces are introduced. Part of these spaces for N=5 are interpreted as the noncommutative analogs of (1+3) space-time models. As a result the wide variety of the quantum deformations of realistic kinematics are suggested.