{"title":"Number-Theory Renormalization of Vacuum Energy","authors":"","doi":"10.1134/s2070046623040039","DOIUrl":null,"url":null,"abstract":"<span> <h3>Abstract</h3> <p> For QFT on a lattice of dimension <span> <span>\\(d\\geqslant 3\\)</span> </span>, the vacuum energy (both bosonic and fermionic) is zero if the Hamiltonian is a function of the square of the momentum, and the calculation of the vacuum energy is performed in the ring of residue classes modulo <span> <span>\\(N\\)</span> </span>. This fact is related to a problem from number theory about the number of ways to represent a number as a sum of <span> <span>\\(d\\)</span> </span> squares in the ring of residue classes modulo <span> <span>\\(N\\)</span> </span>. </p> </span>","PeriodicalId":44654,"journal":{"name":"P-Adic Numbers Ultrametric Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"P-Adic Numbers Ultrametric Analysis and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s2070046623040039","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
For QFT on a lattice of dimension \(d\geqslant 3\), the vacuum energy (both bosonic and fermionic) is zero if the Hamiltonian is a function of the square of the momentum, and the calculation of the vacuum energy is performed in the ring of residue classes modulo \(N\). This fact is related to a problem from number theory about the number of ways to represent a number as a sum of \(d\) squares in the ring of residue classes modulo \(N\).
期刊介绍：
This is a new international interdisciplinary journal which contains original articles, short communications, and reviews on progress in various areas of pure and applied mathematics related with p-adic, adelic and ultrametric methods, including: mathematical physics, quantum theory, string theory, cosmology, nanoscience, life sciences; mathematical analysis, number theory, algebraic geometry, non-Archimedean and non-commutative geometry, theory of finite fields and rings, representation theory, functional analysis and graph theory; classical and quantum information, computer science, cryptography, image analysis, cognitive models, neural networks and bioinformatics; complex systems, dynamical systems, stochastic processes, hierarchy structures, modeling, control theory, economics and sociology; mesoscopic and nano systems, disordered and chaotic systems, spin glasses, macromolecules, molecular dynamics, biopolymers, genomics and biology; and other related fields.
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