Quantization of the Riemann Zeta-Function and Cosmology

Abstract

Quantization of the Riemann zeta-function is proposed. We treat the Riemann zeta-function as a symbol of a pseudodifferential operator and study the corresponding classical and quantum field theories. This approach is motivated by the theory of p-adic strings and by recent works on stringy cosmological models. We show that the Lagrangian for the zeta-function field is equivalent to the sum of the Klein-Gordon Lagrangians with masses defined by the zeros of the Riemann zeta-function. Quantization of the mathematics of Fermat-Wiles and the Langlands program is indicated. The Beilinson conjectures on the values of L-functions of motives are interpreted as dealing with the cosmological constant problem. Possible cosmological applications of the zeta-function field theory are discussed.

14 pages, corrected typos, references and comments added

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Cited by in corpus (22)

• p-Adic Mathematical Physics
• Towards a Resolution of the Cosmological Singularity in Non-local Higher Derivative Theories of Gravity
• Dynamics with Infinitely Many Derivatives: The Initial Value Problem
• $p$-Adic Mathematical Physics: The First 30 Years
• Nonlocal gravity and the diffusion equation
• De Sitter Universe in Nonlocal Gravity
• Super-accelerating bouncing cosmology in asymptotically-free non-local gravity
• Reconstruction Procedure in Nonlocal Cosmological Models
• Cosmological Solutions of a Nonlocal Model with a Perfect Fluid
• Finite quantum gravity in dS and AdS spacetimes
• Dynamics in nonlocal linear models in the Friedmann-Robertson-Walker metric
• Cosmological Daemon
• Cosmological perturbations in SFT inspired non-local scalar field models
• Localization of nonlocal cosmological models with quadratic potentials in the case of double roots
• Analysis of scalar perturbations in cosmological models with a non-local scalar field
• Zeta Nonlocal Scalar Fields
• Effective models of inflation from a non-local framework
• Exact Solutions for Nonlocal Nonlinear Field Equations in Cosmology
• Nonlocal Dynamics of p-Adic Strings
• Localization of the SFT inspired Nonlocal Linear Models and Exact Solutions
• Towards effective Lagrangians for adelic strings
• On p-Adic Sector of Adelic String