Zeta Nonlocal Scalar Fields

Abstract

We consider some nonlocal and nonpolynomial scalar field models originated from p-adic string theory. Infinite number of spacetime derivatives is determined by the operator valued Riemann zeta function through d'Alembertian $\square$ in its argument. Construction of the corresponding Lagrangians L starts with the exact Lagrangian ${\mathcal{L}}_p$ for effective field of p-adic tachyon string, which is generalized replacing p by arbitrary natural number n and then taken a sum of ${\mathcal{L}}_n$ over all n. The corresponding new objects we call zeta scalar strings. Some basic classical field properties of these fields are obtained and presented in this paper. In particular, some solutions of the equations of motion and their tachyon spectra are studied. Field theory with Riemann zeta function dynamics is interesting in its own right as well.

13 pages, submitted to Theoretical and Mathematical Physics

References in corpus (17)

• On Exact Tachyon Potential in Open String Field Theory
• Dynamics with Infinitely Many Time Derivatives and Rolling Tachyons
• On the Nonlinear Dynamical Equation in the p-adic String Theory
• Time Evolution in Open String Theory
• Time Evolution in Superstring Field Theory on non-BPS brane.I. Rolling Tachyon and Energy-Momentum Conservation
• Dynamics with Infinitely Many Derivatives: The Initial Value Problem
• Route to nonlocal cosmology
• Tachyon Condensation and Brane Descent Relations in p-adic String Theory
• p-adic Inflation
• Bouncing and Accelerating Solutions in Nonlocal Stringy Models
• Tachyon condensation in open-closed p-adic string theory
• Nonlinear equations for p-adic open, closed, and open-closed strings
• On the Null Energy Condition and Cosmology
• Quantization of the Riemann Zeta-Function and Cosmology
• Mode Interactions of the Tachyon Condensate in p-adic String Theory
• On the relation between p-adic and ordinary strings
• Towards p-Adic String in Constant B-Field

Cited by in corpus (11)

• p-Adic Mathematical Physics
• Towards a Resolution of the Cosmological Singularity in Non-local Higher Derivative Theories of Gravity
• $p$-Adic Mathematical Physics: The First 30 Years
• Stable analytic bounce in non-local Einstein-Gauss-Bonnet cosmology
• Thermodynamics and Cosmological Constant of Non-Local Field Theories from p-Adic Strings
• Localization of nonlocal cosmological models with quadratic potentials in the case of double roots
• Thermodynamics of String Field Theory Motivated Nonlocal Models
• Nonlocal Dynamics of p-Adic Strings
• The initial value problem for ordinary differential equations with infinitely many derivatives
• Towards effective Lagrangians for adelic strings
• On p-Adic Sector of Adelic String