Number-theory renormalization of vacuum energy

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.

arXiv comment33 pages, 7 figures

References in corpus (1)

• Ternary and Binary Representation of Coordinate and Momentum in Quantum Mechanics

Cited by in corpus (1)

• Digital representation of continuous observables in Quantum Mechanics