Quantization of the Riemann Zeta-Function and Cosmology

Details Quantization of the Riemann Zeta-Function and Cosmology Quantization of the Riemann Zeta-Function and Cosmology

2007-01-30

arxiv.org/abs/hep-th/0701284v2

Int.J.Geom.Meth.Mod.Phys.4:881-895,2007

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, corrected typos, references and comments added

Scientific paper

10.1142/S021988780700234X

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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