Local and Global Casimir Energies: Divergences, Renormalization, and the Coupling to Gravity

Abstract

From the beginning of the subject, calculations of quantum vacuum energies or Casimir energies have been plagued with two types of divergences: The total energy, which may be thought of as some sort of regularization of the zero-point energy, $\sum \frac{1}{2}\hslash \omega$, seems manifestly divergent. And local energy densities, obtained from the vacuum expectation value of the energy-momentum tensor, $⟨T_{00}⟩$, typically diverge near boundaries. The energy of interaction between distinct rigid bodies of whatever type is finite, corresponding to observable forces and torques between the bodies, which can be unambiguously calculated. The self-energy of a body is less well-defined, and suffers divergences which may or may not be removable. Some examples where a unique total self-stress may be evaluated include the perfectly conducting spherical shell first considered by Boyer, a perfectly conducting cylindrical shell, and dilute dielectric balls and cylinders. In these cases the finite part is unique, yet there are divergent contributions which may be subsumed in some sort of renormalization of physical parameters. The divergences that occur in the local energy-momentum tensor near surfaces are distinct from the divergences in the total energy, which are often associated with energy located exactly on the surfaces. However, the local energy-momentum tensor couples to gravity, so what is the significance of infinite quantities here? For the classic situation of parallel plates there are indications that the divergences in the local energy density are consistent with divergences in Einstein's equations; correspondingly, it has been shown that divergences in the total Casimir energy serve to precisely renormalize the masses of the plates, in accordance with the equivalence principle.

53 pages, 1 figure, invited review paper to Lecture Notes in Physics volume in Casimir physics edited by Diego Dalvit, Peter Milonni, David Roberts, and Felipe da Rosa

References in corpus (13)

• Worldline algorithms for Casimir configurations
• How Does Casimir Energy Fall?
• Casimir edge effects
• Multiple Scattering Methods in Casimir Calculations
• Recent Developments in the Casimir Effect
• How does Casimir energy fall? II. Gravitational acceleration of quantum vacuum energy
• Nonmonotonic effects of parallel sidewalls on Casimir forces between cylinders
• Exact Casimir Interaction Between Semitransparent Spheres and Cylinders
• Local and Global Casimir Energies for a Semitransparent Cylindrical Shell
• Casimir Force at a Knife's Edge
• Vacuum Stress and Closed Paths in Rectangles, Pistons, and Pistols
• Perturbative zero-point energy for a cylinder of elliptical section
• Weak Coupling Casimir Energies for Finite Plate Configurations

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• Vacuum Casimir energy densities and field divergences at boundaries
• Vacuum local and global electromagnetic self-energies for a point-like and an extended field source
• Scalar Casimir Energies of Tetrahedra and Prisms
• Casimir Energy Corrections by Light-Cone Fluctuations
• Scarf for Lifshitz
• Archimedes Force on Casimir Apparatus
• Scalar Casimir Energies of Tetrahedra