Quantization of the Riemann Zeta-Function and Cosmology

TL;DR

This paper explores a novel approach to quantizing the Riemann zeta-function by linking it to field theories and cosmological models, inspired by string theory and number theory conjectures.

Contribution

It introduces a framework treating the zeta-function as a pseudodifferential operator, connecting number theory, quantum field theory, and cosmology in a new way.

Findings

Zeta-function field Lagrangian is equivalent to multiple Klein-Gordon fields.

Potential cosmological applications of zeta-function field theory are discussed.

Connections between L-functions, Fermat-Wiles, and the cosmological constant are proposed.

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.