From p-adic to Archimedean Physics: Renormalization Group Flow and Berkovich Spaces

2020/01/06 by An Huang, Dan Mao, Huang, An +3 · 2 citations
Computer Science · Mathematics · #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Number Theory (math.NT) #Topological and Geometric Data Analysis #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2001.01725

openalex publication_date 2020/01/06 · openalex created_date 2020/01/23 · openalex updated_date 2026/07/28

Abstract

We introduce the p-adic particle-in-a-box as a free particle with periodic boundary conditions in the p-adic spatial domain. We compute its energy spectrum, and show that the spectrum of the Archimedean particle-in-a-box can be recovered from the p-adic spectrum via an Euler product formula. This product formula arises from a flow equation in Berkovich space, which we interpret as a space of theories connected by a kind of renormalization group flow. We propose that Berkovich spaces can be used to relate p-adic and Archimedean quantities generally.

Citations

• Tensor networks, p-adic fields, and algebraic curves: arithmetic and the AdS₃/CFT₂ correspondence

Cited by

• Bounds on the Ricci curvature and solutions to the Einstein equations for weighted graphs
• Massless p2-brane modes and the critical line

Related

• A massless quantum field theory over the p-adics
• Non-Archimedean Coulomb Gases
• Introduction to the p-adic Space
• Non-Archimedean Statistical Field Theory
• On ℙ_Berk¹ and Coarse-Grainings of Non-Archimedean Product Spaces