Roberto Passante, Lucia Rizzuto, Salvatore Spagnolo
We consider vacuum electric and magnetic energy densities (or equivalently field fluctuations) in the space around a point-like or an extended ground-state field source, and discuss the problem of their singular behavior at the source's position. We show that the assumption of point-like source leads to a divergence of the renormalized energy densities at the position of the source and analyze in detail the structure of such singularity in terms of a delta function and its derivatives. We then consider the case of an extended source, smeared out over a finite volume and described by an appropriate form factor, and show that in this case all divergences in the local energy densities are removed. Our results for the structure of the divergences in the field energy densities also resolve an apparent inconsistency between the vacuum expectation value of the field Hamiltonian and of the field energy densities integrated over all space.
View original:
http://arxiv.org/abs/1208.5478
No comments:
Post a Comment