Number-theory renormalization of vacuum energy

For QFT on a lattice of dimension d>=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 numb...

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Bibliographic Details
Published inarXiv.org
Main Authors Ivanov, M G, Dudchenko, V A, Naumov, V V
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 21.07.2023
Subjects
Hamiltonian functions
Number theory
Residues
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Summary:For QFT on a lattice of dimension d>=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.
ISSN:2331-8422