Quantum Spacetime Pictures and Dynamics from a Relativity Perspective

TL;DR

This paper develops a quantum model of physical space based on quantum relativity symmetry, linking noncommutative spacetime with classical Newtonian and relativistic frameworks, and discusses its dynamical and covariant extensions.

Contribution

It introduces a quantum spacetime model derived from quantum relativity symmetry and extends it to Lorentz covariant settings, bridging classical and quantum descriptions.

Findings

Quantum relativity symmetry contraction yields Newtonian approximation.

Observable algebra matches the group C*-algebra representation.

Extension to Lorentz covariant and noncommutative spacetime frameworks.

Abstract

Based on an identified quantum relativity symmetry the contraction of which gives the Newtonian approximation of Galilean relativity, a quantum model of the physical space can be formulated with the Newtonian space seen in a way as the classical approximation. Matching picture for the observable algebra as the corresponding representation of the group C* -algebra, describes the full dynamical pictures equally successfully. Extension of the scheme to a Lorentz covariant setting and beyond will also be addressed.The formulation of quantum mechanics allows the theory to be seen in a new picture in line with the notion of a noncommutative spacetime.