How does Casimir energy fall? IV. Gravitational interaction of regularized quantum vacuum energy
Abstract
Several years ago we demonstrated that the Casimir energy for perfectly reflecting and imperfectly reflecting parallel plates gravitated normally, that is, obeyed the equivalence principle. At that time the divergences in the theory were treated only formally, without proper regularization, and the coupling to gravity was limited to the canonical energymomentumstress tensor. Here we strengthen the result by removing both of those limitations. We consider, as a toy model, massless scalar fields interacting with semitransparent (δfunction) potentials defining parallel plates, which become Dirichlet plates for strong coupling. We insert space and time pointsplit regulation parameters, and obtain welldefined contributions to the selfenergy of each plate, and the interaction energy between the plates. (This selfenergy does not vanish even in the conformally coupled, strongcoupled limit.) We also compute the local energy density, which requires regularization near the plates. In general, the energy density includes a surface energy that resides precisely on the boundaries. This energy is also regulated. The gravitational interaction of this welldefined system is then investigated, and it is verified that the equivalence principle is satisfied.
 Publication:

Physical Review D
 Pub Date:
 March 2014
 DOI:
 10.1103/PhysRevD.89.064027
 arXiv:
 arXiv:1401.0784
 Bibcode:
 2014PhRvD..89f4027M
 Keywords:

 04.62.+v;
 04.20.Cv;
 03.70.+k;
 11.10.Gh;
 Quantum field theory in curved spacetime;
 Fundamental problems and general formalism;
 Theory of quantized fields;
 Renormalization;
 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology;
 Quantum Physics
 EPrint:
 14 pages, 4 figures