Journal
INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
Volume 4, Issue 5, Pages 881-895Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S021988780700234X
Keywords
zeta-function; quantization; cosmology
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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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