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arXiv · 2307.11691

Number-theory renormalization of vacuum energy

M. G. Ivanov·V. A. Dudchenko·V. V. Naumov
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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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M. G. Ivanov, V. A. Dudchenko, V. V. Naumov. 2023-07-21. Number-theory renormalization of vacuum energy. https://doi.org/10.1134/s2070046623040039

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