Geodesic
$p$-adic space-time and string theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 71 (1987) no. 3, pp. 337-340

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Arguments are presented in favour of the hypothesis suggesting the $p$-adic structure of the space-time. A $p$-adic analogue of the Veneziano amplitude is suggested which makes it possible to start the construction of the theory of $p$-adic strings. The same problems are considered over Galois fields in which case the analogue of the Veneziano amplitude is the Jacobi sum expressed in terms of $l$-adic cohomologies of Fermat curves. An expression for the vertex operator of corresponding string theory is given. 
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     author = {I. V. Volovich},
     title = {$p$-adic space-time and string theory},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {337--340},
     publisher = {mathdoc},
     volume = {71},
     number = {3},
     year = {1987},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1987_71_3_a2/}
}
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I. V. Volovich. $p$-adic space-time and string theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 71 (1987) no. 3, pp. 337-340. http://geodesic.mathdoc.fr/item/TMF_1987_71_3_a2/