Effective Lagrangians for p-Adic and Zeta Strings
The effective Lagrangian for open p-adic string tachyon describes its all
tree-level scattering amplitudes. It also reproduces some nontrivial
features of ordinary string theory. This Lagrangian depends on prime number
p and makes sense for any natural number n. Appropriate summation over n
gives an effective Lagrangian with spacetime derivatives encoded in the
operator valued Riemann zeta function. Various
properties of the related zeta strings are obtained.