Investigations of the torque anomaly in an annular sector. I. Global calculations, scalar case

Milton, Kimball A.; Kheirandish, Fardin; Parashar, Prachi; Abalo, E. K.; Fulling, S. A.; Bouas, J D; Carter, Hamilton; Kirsten, Klaus

doi:10.1103/physrevd.88.025039

Cited by 10 publications

(11 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(2.31) have been taken. To understand the pressure anomaly it is essential, though, to consider point-splitting in an arbitrary direction in the (τ, r ⊥ ) 3-space [12,20]. Putting Eqs.…”

Section: B Stress Tensormentioning

confidence: 99%

Vacuum energy density and pressure near a soft wall

et al. 2016

View full text Add to dashboard Cite

Perfectly conducting boundaries, and their Dirichlet counterparts for quantum scalar fields, predict nonintegrable energy densities. A more realistic model with a finite ultraviolet cutoff yields two inconsistent values for the force on a curved or edged boundary (the "pressure anomaly"). A still more realistic, but still easily calculable, model replaces the hard wall by a power-law potential; because it involves no a posteriori modification of the formulas calculated from the theory, this model should be anomaly-free. Here we first set up the formalism and notation for the quantization of a scalar field in the background of a planar soft wall, and we approximate the reduced Green function in perturbative and WKB limits (the latter being appropriate when either the mode frequency or the depth into the wall is sufficiently large). Then we display numerical calculations of energy density and pressure for the region outside the wall, which show that the pressure anomaly does not occur there. Calculations inside the wall are postponed to later papers, which must tackle regularization and renormalization of divergences induced by the potential in the bulk region.

show abstract

“…(2.31) have been taken. To understand the pressure anomaly it is essential, though, to consider point-splitting in an arbitrary direction in the (τ, r ⊥ ) 3-space [12,20]. Putting Eqs.…”

Section: B Stress Tensormentioning

confidence: 99%

Vacuum energy density and pressure near a soft wall

et al. 2016

View full text Add to dashboard Cite

show abstract

“…We considered an infinitesimally thin translucent plane surface and learned that the permittivity and permeability potentials were necessarily anisotropic. Here, we adapt that formalism to spherical geometry; in addition, we regulate the frequency integrals and angular momentum sums by introducing temporal and spatial point-splitting regulators, which turned out to be extremely effective in geometries with curvature and corner divergences [25,26]. Specifically, we keep both temporal and spatial point-splitting cutoffs, which were proposed as a tool for a systematic analysis in the context of the principle of virtual work in Refs.…”

Section: Introductionmentioning

confidence: 99%

Electromagnetic δ -function sphere

et al. 2017

Self Cite

View full text Add to dashboard Cite

We develop a formalism to extend our previous work on the electromagnetic δ-function plates to a spherical surface. The electric (λe) and magnetic (λg) couplings to the surface are through δ-function potentials defining the dielectric permittivity and the diamagnetic permeability, with two anisotropic coupling tensors. The formalism incorporates dispersion. The electromagnetic Green's dyadic breaks up into transverse electric and transverse magnetic parts. We derive the Casimir interaction energy between two concentric δ-function spheres in this formalism and show that it has the correct asymptotic flat plate limit. We systematically derive expressions for the Casimir self-energy and the total stress on a spherical shell using a δ-function potential, properly regulated by temporal and spatial point-splitting, which are different from the conventional temporal pointsplitting. In strong coupling, we recover the usual result for the perfectly conducting spherical shell but in addition there is an integrated curvature-squared divergent contribution. For finite coupling, there are additional divergent contributions; in particular, there is a familiar logarithmic divergence occurring in the third order of the uniform asymptotic expansion that renders it impossible to extract a unique finite energy except in the case of an isorefractive sphere, which translates into λg = −λe.

show abstract

“…In I we showed that 8) and in just the same way we can show [15] 9) in terms of the quantities defined in Eq. (3.6).…”

Section: Annular Sectormentioning

confidence: 64%

“…In Ref. [8] we considered such a geometry for a massless scalar field, with Dirichlet boundaries. We regulate the integral by point-splitting in the time or the axial direction.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Investigations of the torque anomaly in an annular sector. II. Global calculations, electromagnetic case

et al. 2013

Self Cite

View full text Add to dashboard Cite

Recently, it was suggested that there was some sort of breakdown of quantum field theory in the presence of boundaries, manifesting itself as a torque anomaly. In particular, Fulling et al. used the finite energy-momentum-stress tensor in the presence of a perfectly conducting wedge, calculated many years ago by Deutsch and Candelas, to compute the torque on one of the wedge boundaries, where the latter was cutoff by integrating the torque density down to minimum lower radius greater than zero. They observed that that torque is not equal to the negative derivative of the energy obtained by integrating the energy density down to the same minimum radius. This motivated a calculation of the torque and energy in an annular sector obtained by the intersection of the wedge with two coaxial cylinders. In a previous paper we showed that for the analogous scalar case, which also exhibited a torque anomaly in the absence of the cylindrical boundaries, the point-split regulated torque and energy indeed exhibit an anomaly, unless the point-splitting is along the axis direction. In any case, because of curvature divergences, no unambiguous finite part can be extracted. However, that ambiguity is linear in the wedge angle; if the condition is imposed that the linear term be removed, the resulting torque and energy is finite, and exhibits no anomaly. In this paper, we demonstrate the same phenomenon takes place for the electromagnetic field, so there is no torque anomaly present here either. This is a nontrivial generalization, since the anomaly found by Fulling et al. is linear for the Dirichlet scalar case, but nonlinear for the conducting electromagnetic case.

show abstract

Investigations of the torque anomaly in an annular sector. I. Global calculations, scalar case

Cited by 10 publications

References 31 publications

Vacuum energy density and pressure near a soft wall

Vacuum energy density and pressure near a soft wall

Electromagnetic δ -function sphere

Investigations of the torque anomaly in an annular sector. II. Global calculations, electromagnetic case

Contact Info

Product

Resources

About