Green's functions for Vladimirov derivatives and Tate's thesis

DOI10.4310/CNTP.2021.V15.N2.A3zbMATH Open1471.11281arXiv2001.01721MaRDI QIDQ2041580

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Publication date: 23 July 2021

Published in: (Search for Journal in Brave)

Abstract: Given a number field $K$ with a Hecke character $chi$, for each place $u$ 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 $u$, 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.

Full work available at URL: https://arxiv.org/abs/2001.01721

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