Complete Zeta-Function Approach to the Electromagnetic Casimir Effect for Spheres and Circles

Leseduarte, S.; Romeo, August

doi:10.1006/aphy.1996.0101

Cited by 85 publications

(139 citation statements)

References 46 publications

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“…The first complete calculation for the massive case was done in [33] for a scalar field and in [128] for a spinor field with bag boundary conditions. In [140] the results for a massless field in several dimensions are collected. A calculation of the Casimir energy in any (even fractional) dimension is done in [141,142].…”

Section: Results On the Casimir Effect On A Spherementioning

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: Results On the Casimir Effect On A Spherementioning

confidence: 99%

“…As a result it follows from Eq. (4.137) 140) t being measured in seconds, which results in approximatelly 4 × 10 4 photons created in the cavity during one second due to the wall oscillations. So large number of photons can be observed experimentally.…”

Section: Dynamical Casimir Effectmentioning

confidence: 99%

New developments in the Casimir effect

2001

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“…In particular, the generalized zeta function method [19,20] is in general very powerful to give physical meaning to the divergent quantities. There are several examples of the application of this method to the evaluation of the Casimir effect (see, for instance, [7,20,21,22,23,24,25,26,27,28,29,30]). In this paper, by using the zeta function technique, we consider the Casimir energy for the geometries of a single and two parallel plates, moving by uniform proper acceleration through the Fulling-Rindler vacuum.…”

Section: Introductionmentioning

confidence: 99%

Casimir energy in the Fulling-Rindler vacuum

2004

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The Casimir energy is evaluated for massless scalar fields under Dirichlet or Neumann boundary conditions, and for the electromagnetic field with perfect conductor boundary conditions on one and two infinite parallel plates moving by uniform proper acceleration through the Fulling-Rindler vacuum in an arbitrary number of spacetime dimension. For the geometry of a single plate both regions of the right Rindler wedge, (i) on the right (RR region) and (ii) on the left (RL region) of the plate are considered. The zeta function technique is used, in combination with contour integral representations. The Casimir energies for separate RR and RL regions contain pole and finite contributions. For an infinitely thin plate taking RR and RL regions together, in odd spatial dimensions the pole parts cancel and the Casimir energy for the whole Rindler wedge is finite. In d = 3 spatial dimensions the total Casimir energy for a single plate is negative for Dirichlet scalar and positive for Neumann scalar and the electromagnetic field. The total Casimir energy for two plates geometry is presented in the form of a sum of the Casimir energies for separate plates plus an additional interference term. The latter is negative for all values of the plates separation for both Dirichlet and Neumann scalars, and for the electromagnetic field.

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“…f n e i(n+ (27) and APS boundary conditions must be reversed, for λ = 0, as compared to (20), since the operator B changes into −B. For λ = 0 the lower component will be taken to be zero at r 0 which, as we will show later, allows for charge conjugation to be a symmetry of the whole model.…”

Section: Boundary Conditions At the Originmentioning

confidence: 99%

“…V, we determine the energy spectrum and study the fermionic number and Casimir energy of the confined system. This last calculation is performed in a ζ function approach, following the lines of reference [20].…”

Section: Introductionmentioning

confidence: 99%

Dirac Fields in the Background of a Magnetic Flux String and Spectral Boundary Conditions

Beneventano

Francia

Santangelo

1999

Int. J. Mod. Phys. A

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We study the problem of a Dirac field in the background of an Aharonov-Bohm flux string. We exclude the origin by imposing spectral boundary conditions at a finite radius then shrinked to zero. Thus, we obtain a behaviour of the eigenfunctions which is compatible with the self-adjointness of the radial Hamiltonian and the invariance under integer translations of the reduced flux.After confining the theory to a finite region, we check the consistency with the index theorem, and evaluate its vacuum fermionic number and Casimir energy.

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Complete Zeta-Function Approach to the Electromagnetic Casimir Effect for Spheres and Circles

Cited by 85 publications

References 46 publications

New developments in the Casimir effect

New developments in the Casimir effect

Casimir energy in the Fulling-Rindler vacuum

Dirac Fields in the Background of a Magnetic Flux String and Spectral Boundary Conditions

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