Number-Theory Renormalization of Vacuum Energy.

For QFT on a lattice of dimension , 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 . This fact is related to a problem from number theory about the number of ways to represent a number as a sum of squares in the ring of residue classes modulo . [ABSTRACT FROM AUTHOR]