Geodesic
Arithmetic Quantum Physics: Why, What, and Whither
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected topics of $p$-adic mathematical physics and analysis, Tome 245 (2004), pp. 273-280

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This article contains a discussion of some of the motivations for doing quantum physics in arithmetic contexts such as $p$-adic and adelic spaces, a brief survey of some of the results obtained so far, and some indications of directions of future research, including some open problems and speculations at the end. 
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     author = {V. S. Varadarajan},
     title = {Arithmetic {Quantum} {Physics:} {Why,} {What,} and {Whither}},
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V. S. Varadarajan. Arithmetic Quantum Physics: Why, What, and Whither. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected topics of $p$-adic mathematical physics and analysis, Tome 245 (2004), pp. 273-280. http://geodesic.mathdoc.fr/item/TM_2004_245_a27/