Towards Adelic Noncommutative Quantum Mechanics
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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.
KeywordsStar Product Deformation Quantization Ultrametric Space Canonical Commutation Relation Standard Quantum Mechanic
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