Relativity Symmetry Contraction and Quantum Spacetime Ii

This is an extension of the current grant project which is a real breakthrough step within a long term program, both in terms of important results obtained and new directions identified. The big final goal of the program effort is to find the right model for the deep microscopic quantum spacetime and build the theory of its dynamics. We have just obtained a first model of quantum space together with a full description of the dynamical theory as ordinary quantum mechanics in the language of representation of the group C*-algebra as the observable algebra matching to the quantum space as a representation of the relativity group. Approximate theory is successfully formulated through relativity symmetry contraction, retrieving the full classical limit as Newtonian mechanics on the Newtonian space and dynamics. Another direction is the similar formulation with Einstein special relativity incorporated, with its explicit contraction to the classical Minkowski spacetime picture as well as contraction to the quantum space of the extended Galilean setting before going to Newtonian. To the latter, we have finished the relativity symmetry and coset space representation part with the grand scheme on step-by-step contraction from the earlier identified fundamental Quantum Relativity symmetry. We will further explore all those pictures in the Hilbert space, pure algebraic, and noncommutative geometric language, as preparation for going to the deep microscopic regime. We have already achieved a big success with great implications to a better understanding of quantum mechanics, though still to be recognized. We expect other important results to follow in the coming year.