Quantization of the Riemann Zeta-Function and Cosmology

I. Ya. Aref'eva; I. V. Volovich

doi:10.1142/s021988780700234x

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arXiv · hep-th/0701284

Quantization of the Riemann Zeta-Function and Cosmology

I. Ya. Aref'eva·I. V. Volovich

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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.

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I. Ya. Aref'eva, I. V. Volovich. 2007-02-05. Quantization of the Riemann Zeta-Function and Cosmology. https://doi.org/10.1142/s021988780700234x

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