這是本年度計劃的延伸, 無論是在取得的重要成果和看到的新方向方面,也是我們長期研究計劃的真正突破性一步.此計劃的最終目標在於找到微觀量子時空的模型並且建構量子時空動力學理論的正確模型．我們已經從相對論對稱獲得一個普通量子力學後面的量子空間的模型，並且對其可觀察量代數和其動力學給出全面的描述, 並以對稱收縮成功明確描述作為其近似古典的牛頓物理圖像．另一個研究方向則是符合愛因斯坦狹義相對論的類似理論架構; 明確描述其對稱收縮到古典閔可夫斯基時空相對論力學,普通(延伸伽利略對稱)量子力學,以及牛頓物理的圖像．在這方面, 我們已經從先前確定的基本量子相對論對稱性逐步收縮的宏觀方案完成了相對論對稱性和陪集空間表示部分。我們也將開始探索這些理論結構在純代數和反對易幾何語言的描述，來為更深入地探索微觀量子時空的物理做準備．我們已經取得了巨大的成功，對於更好地理解量子力學有很大的啟示，儘管還有待認識。 我們預計明年將會有其他重要成果。 ;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.
