真空能量的数论重正化

IF 0.5 Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

P-Adic Numbers Ultrametric Analysis and Applications Pub Date : 2023-12-01 DOI:10.1134/s2070046623040039

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引用次数: 0

摘要

摘要对于维数为 \(d\geqslant 3\) 的晶格上的 QFT，如果哈密顿是动量平方的函数，那么真空能（玻色和费米子）为零，并且真空能的计算是在（N）模的残差类环中进行的。这一事实与数论中的一个问题有关，即在模（N）的残差类环中将一个数表示为（d）平方和的方法有多少种。

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Number-Theory Renormalization of Vacuum Energy

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 \(N\) .

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来源期刊

P-Adic Numbers Ultrametric Analysis and Applications MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

1.10

自引率

20.00%

发文量

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.