Zeta-nonlocal scalar fields
Teoretičeskaâ i matematičeskaâ fizika, Tome 157 (2008) no. 3, pp. 364-372
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We consider some nonlocal and nonpolynomial scalar field models originating from $p$-adic string theory. An infinite number of space-time derivatives is determined by the operator-valued Riemann zeta function through the d'Alembertian $\Box$ in its argument. The construction of the corresponding Lagrangians $L$ starts with the exact Lagrangian $\mathcal L_p$ for the effective field of the $p$-adic tachyon string, which is generalized by replacing $p$ with an arbitrary natural number $n$ and then summing $\mathcal L_n$ over all $n$. We obtain several basic classical properties of these fields. In particular, we study some solutions of the equations of motion and their tachyon spectra. The field theory with Riemann zeta-function dynamics is also interesting in itself.
Keywords:
nonlocal field theory, $p$-adic string theory, Riemann zeta function.
@article{TMF_2008_157_3_a3,
author = {B. G. Dragovich},
title = {Zeta-nonlocal scalar fields},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {364--372},
publisher = {mathdoc},
volume = {157},
number = {3},
year = {2008},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2008_157_3_a3/}
}
B. G. Dragovich. Zeta-nonlocal scalar fields. Teoretičeskaâ i matematičeskaâ fizika, Tome 157 (2008) no. 3, pp. 364-372. http://geodesic.mathdoc.fr/item/TMF_2008_157_3_a3/