Number-theory renormalization of vacuum energy

Author:

M. G. Ivanov, V. A. Dudchenko, V. V. Naumov

Keyword:

High Energy Physics - Lattice, High Energy Physics - Lattice (hep-lat), Number Theory (math.NT)

journal:

date:

2023-07-20 16:00:00

Abstract

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.

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