Towards Adelic Noncommutative Quantum Mechanics

Details Towards Adelic Noncommutative Quantum Mechanics Towards Adelic Noncommutative Quantum Mechanics

2004-12-08

arxiv.org/abs/hep-th/0412088v1

CRM Springer Lecture Notes in Physics, 616 (2003) 25-32, Editors: J. Trampetic and J. Wess

Physics

High Energy Physics

High Energy Physics - Theory

8 pages, Talk presented at the 8th Adriatic Meeting, "Particle Physics in the new Millennium", (Dubrovnik, Croatia)

Scientific paper

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.

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