Comment on contributions of fundamental particles to the vacuum energy

This is the comment to the preprints by G. Ossola and A. Sirlin, hep-ph/0305050, and E.Kh. Akhmedov, hep-th/0204048, who discussed different regularization schemes for calculations of the vacuum energy stored in the zero-point motion of fundamental fields. We show that the contribution of the fermionic and bosonic fields to the energy of the vacuum depends on the physical realization of the vacuum state. The energy density of the homogeneous vacuum is zero irrespective of the fermionic and bosonic content of the effective theories in the infra-red corner. The contribution of the low-energy fermions and bosons becomes important when the coexistence of different vacua is considered , such as the bubble of the true vacuum inside the false one, We consider the case when these vacua differ only by the masses of the low-energy fermionic fields, M true > M false , while their ultraviolet structure is identical. In this geometry the energy density of the false vacuum outside the bubble is zero, ρ false = −P false = 0, which corresponds to zero cosmological constant. The energy density of the true vacuum inside the bubble is ρ true = −P true ∝ −Λ 2 (M 2 true − M 2 false), where Λ is the ultraviolet cutoff .