Towards effective Lagrangians for adelic strings

Dragovich, Branko
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p-Adic strings are important objects of string theory, as well as of p-adic mathematical physics and nonlocal cosmology. By a concept of adelic string one can unify and simultaneously study various aspects of ordinary and p-adic strings. By this way, one can consider adelic strings as a very useful instrument in the further investigation of modern string theory. It is remarkable that for some scalar p-adic strings exist effective Lagrangians, which are based on real instead of p-adic numbers and describe not only four-point scattering amplitudes but also all higher ones at the tree level. In this work, starting from p-adic Lagrangians, we consider some approaches to construction of effective field Lagrangians for p-adic sector of adelic strings. It yields Lagrangians for nonlinear and nonlocal scalar field theory, where spacetime nonlocality is determined by an infinite number of derivatives contained in the operator-valued Riemann zeta function. Owing to the Riemann zeta function in the dynamics of these scalar field theories, obtained Lagrangians are also interesting in themselves.
Comment: 11 pages. Based on a talk at the 4-th RTN "Forces-Universe" EU Network Workshop in Varna, 11-17 September 2008. Submitted for publication to the Fortschritte der Physik
High Energy Physics - Theory, Mathematical Physics