Ground state energy for a penetrable sphere and for a dielectric ball

Bordag, M.; Kirsten, Klaus; Vassilevich, D. V.

doi:10.1103/physrevd.59.085011

Cited by 175 publications

(254 citation statements)

References 31 publications

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“…As it is shown in [82] a ground state energy normalized according to (3.83) doesn't have a finite limit for m → 0 except for the case of a vanishing heat kernel coefficient a 2 . Therefore, in the case of a 2 = 0, the ground state energy of a massless field cannot be uniquely defined and, hence, it is physically meaningless.…”

Section: Renormalization and Normalization Conditionmentioning

confidence: 99%

“…Other coefficients may be present, for instance those with half integer numbers in case of a singular background field, say containing a delta function as considered e.g. in [82]. The best known example is half-classical gravity.…”

Section: Renormalization and Normalization Conditionmentioning

confidence: 99%

“…The coefficients for the penetrable sphere where first calculated in [82] and generalized to an arbitrary penetrable surface in [83]. The coefficients for the dielectric ball are given in [82]. They don't have an explicit expression.…”

Section: The Heat Kernel Expansionmentioning

confidence: 99%

“…In [81] the coefficients for a d-dimensional sphere with Dirichlet and Robin boundary conditions are given up to n = 10. The coefficients for the penetrable sphere where first calculated in [82] and generalized to an arbitrary penetrable surface in [83]. The coefficients for the dielectric ball are given in [82].…”

Section: The Heat Kernel Expansionmentioning

confidence: 99%

“…The heat kernel coefficients have been calculated in [82] with the result that a 2 is in general nonzero. It vanishes only in the dilute approximation, i.e., for small ǫ − 1 respectively for small difference in the speeds of light c 1 and c 2 inside and outside the ball.…”

Section: Rmentioning

confidence: 99%

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New developments in the Casimir effect

2001

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We provide a review of both new experimental and theoretical developments in the Casimir effect. The Casimir effect results from the alteration by the boundaries of the zero-point electromagnetic energy. Unique to the Casimir force is its strong dependence on shape, switching from attractive to repulsive as function of the size, geometry and topology of the boundary. Thus the Casimir force is a direct manifestation of the boundary dependence of quantum vacuum. We discuss in depth the general structure of the infinities in the field theory which are removed by a combination of zeta-functional regularization and heat kernel expansion. Different representations for the regularized vacuum energy are given. The Casimir energies and forces in a number of configurations of interest to applications are calculated. We stress the development of the Casimir force for real media including effects of nonzero temperature, finite conductivity of the boundary metal and surface roughness. Also the combined effect of these important factors is investigated in detail on the basis of condensed matter physics and quantum field theory at nonzero temperature. The experiments on measuring the Casimir force are also reviewed, starting first with the older measurements and finishing with a detailed presentation of modern precision experiments. The latter are accurately compared with the theoretical results for real media. At the end of the review we provide the most recent constraints on the corrections to Newtonian gravitational law and other hypothetical long-range interactions at submillimeter range obtained from the Casimir force measurements.

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Section: Renormalization and Normalization Conditionmentioning

confidence: 99%

Section: Renormalization and Normalization Conditionmentioning

confidence: 99%

Section: The Heat Kernel Expansionmentioning

confidence: 99%

Section: The Heat Kernel Expansionmentioning

confidence: 99%

Section: Rmentioning

confidence: 99%

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New developments in the Casimir effect

2001

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Casimir Effect: The Classical Limit

2001

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We analyze the high temperature (or classical) limit of the Casimir effect. A useful quantity which arises naturally in our discussion is the ``relative Casimir energy", which we define for a configuration of disjoint conducting boundaries of arbitrary shapes, as the difference of Casimir energies between the given configuration and a configuration with the same boundaries infinitely far apart. Using path integration techniques, we show that the relative Casimir energy vanishes exponentially fast in temperature. This is consistent with a simple physical argument based on Kirchhoff's law. As a result the ``relative Casimir entropy", which we define in an obviously analogous manner, tends, in the classical limit, to a finite asymptotic value which depends only on the geometry of the boundaries. Thus the Casimir force between disjoint pieces of the boundary, in the classical limit, is entropy driven and is governed by a dimensionless number characterizing the geometry of the cavity. Contributions to the Casimir thermodynamical quantities due to each individual connected component of the boundary exhibit logarithmic deviations in temperature from the behavior just described. These logarithmic deviations seem to arise due to our difficulty to separate the Casimir energy (and the other thermodynamical quantities) from the ``electromagnetic'' self-energy of each of the connected components of the boundary in a well defined manner. Our approach to the Casimir effect is not to impose sharp boundary conditions on the fluctuating field, but rather take into consideration its interaction with the plasma of ``charge carriers'' in the boundary, with the plasma frequency playing the role of a physical UV cutoff. This also allows us to analyze deviations from a perfect conductor behavior.Comment: latex, 56 pages, one eps figure. Major improvements of presentation (especially in Section 2). No change in the conclusions. Connection with the works of Balian et al. on the Casimir effect is clarified. Abstract changed, typos correcte

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

Milton

2011

Casimir Physics

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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, ∑ 1 2h ω, seems manifestly divergent. And local energy densities, obtained from the vacuum expectation value of the energy-momentum tensor, T 00 , typically diverge near boundaries. These two types of divergences have little to do with each other. 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 divergent local energy densities near surfaces do not change when the relative position of the rigid bodies is altered. 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 finiteness of self-energies is separate from the issue of the physical observability of the effect. 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. This should be a general property, but has not yet been established, for 1 2 Kimball A. Milton example, for the Boyer sphere. It is known that such local divergences can have no effect on macroscopic causality.

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Ground state energy for a penetrable sphere and for a dielectric ball

Cited by 175 publications

References 31 publications

New developments in the Casimir effect

New developments in the Casimir effect

Casimir Effect: The Classical Limit

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

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