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

Jan 6, 2020

43 pages

Published in:

Commun.Num.Theor.Phys. 15 (2021) 2, 315-361

Published: 2021

e-Print:

2001.01721 [hep-th]

DOI:

10.4310/CNTP.2021.v15.n2.a3

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Abstract: (International Press)

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.

Note:

43 pages, matches published version

Vladimirov derivative
Tate’s thesis
Green’s function
adelic product formula
field theory: scalar
field theory: conformal
regularization
adelic
AdS/CFT correspondence
two-point function

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