Nonexistence of solutions of the~$p$-adic strings
Teoretičeskaâ i matematičeskaâ fizika, Tome 174 (2013) no. 2, pp. 208-215
Voir la notice de l'article provenant de la source Math-Net.Ru
We discuss mathematical aspects of the nonexistence of continuous (nontrivial) solutions of boundary value problems for equations of $p$-adic closed and open strings in the one-dimensional case. We find that the number of sign changes of the solution $\psi(t)$ is not equal to the order of zeros of the function $\psi^n(t)$ and that nonnegative (nonpositive) solutions do not exist. In the case of even $n$, if a solution $\psi$ exists, then the orders of zeros of the function $\psi^n$ and the order of its tangency to positive maximums (minimums) are not divisible by four and therefore have the form $2(2r+1)$, $r\ge0$.
Keywords:
$p$-adic string, tachyon, pseudodifferential operator.
@article{TMF_2013_174_2_a1,
author = {V. S. Vladimirov},
title = {Nonexistence of solutions of the~$p$-adic strings},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {208--215},
publisher = {mathdoc},
volume = {174},
number = {2},
year = {2013},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2013_174_2_a1/}
}
V. S. Vladimirov. Nonexistence of solutions of the~$p$-adic strings. Teoretičeskaâ i matematičeskaâ fizika, Tome 174 (2013) no. 2, pp. 208-215. http://geodesic.mathdoc.fr/item/TMF_2013_174_2_a1/