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arXiv · 2001.01721

Green's Functions for Vladimirov Derivatives and Tate's Thesis

An Huang·Bogdan Stoica·Shing-Tung Yau·Xiao Zhong
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Abstract

Given a number field $K$ with a Hecke character $\chi$, for each place $\nu$ we study the free scalar field theory whose kinetic term is given by the regularized Vladimirov derivative associated to the local component of $\chi$. These theories appear in the study of $p$-adic string theory and $p$-adic AdS/CFT correspondence. We prove a formula for the regularized Vladimirov derivative in terms of the Fourier conjugate of the local component of $\chi$. We find that the Green's function is given by the local functional equation for Zeta integrals. Furthermore, considering all places $\nu$, the field theory two-point functions corresponding to the Green's functions satisfy an adelic product formula, which is equivalent to the global functional equation for Zeta integrals. In particular, this points out a role of Tate's thesis in adelic physics.

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An Huang, Bogdan Stoica, Shing-Tung Yau, Xiao Zhong. 2020-01-06. Green's Functions for Vladimirov Derivatives and Tate's Thesis. https://arxiv.org/abs/2001.01721

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