2004/12/08 by Goran S. Djordjevic, Ljubisa Nesic
Physics and Astronomy · Mathematics · #hep-th #math-ph #math.MP
published as CRM Springer Lecture Notes in Physics, 616 (2003) 25-32, Editors: J. Trampetic and J. Wess · 8 pages, Talk presented at the 8th Adriatic Meeting, "Particle Physics in the new Millennium", (Dubrovnik, Croatia)
arxiv created 2004/12/08 · arxiv updated 2009/12/01
A motivation of using noncommutative and nonarchimedean geometry on very short distances is given. Besides some mathematical preliminaries, we give a short introduction in adelic quantum mechanics. We also recall to basic ideas and tools embedded in q-deformed and noncommutative quantum mechanics. A rather fundamental approach, called deformation quantization, is noted. A few relations between noncommutativity and nonarchimedean spaces as well as similarities between corresponding quantum theories on them are pointed out. An extended Moyal product in a proposed form of adelic noncommutative quantum mechanics is considered. We suggest some question for future investigations.