QED vacuum between a conducting and a permeable plate

Cougo-Pinto, M. V.; Farina, C.; Santos, F. C.; Tort, A. C.

doi:10.1088/0305-4470/32/24/311

Cited by 24 publications

(25 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the next section we will evaluate and regularize these correlators by means of analitycal continuation techniques [13] similar, though not equal, to the ones employed by Lütken e Ravndal [16]. We will also show how to obtain the corresponding results for another unusual but intersting setup [13].…”

Section: Maxwell Stress Tensor and The Electromagnetic Field Corrmentioning

confidence: 99%

Electromagnetic field correlators, Maxwell stress tensor, and the Casimir effect for parallel walls

Santos¹,

Sobrinho²,

Tort³

2005

Braz. J. Phys.

View full text Add to dashboard Cite

We evaluate the quantum electromagnetic field correlators associated with the electromagnetic vacuum distorted by the presence of two plane parallel conducting walls and in the presence of a conducting wall parallel to a perfectly magnetically permeable one. Regularization is performed through the generalized zeta funtion technique. Results are applied to rederive the atractive and repulsive Casimir effect through Maxwell stress tensor. Surface divergences are shown to cancel out when stresses on both sides of the material surface are taken into account.

show abstract

Section: Maxwell Stress Tensor and The Electromagnetic Field Corrmentioning

confidence: 99%

Electromagnetic field correlators, Maxwell stress tensor, and the Casimir effect for parallel walls

Santos¹,

Sobrinho²,

Tort³

2005

Braz. J. Phys.

View full text Add to dashboard Cite

show abstract

“…A regularization recipe will also be necessary. Fortunately these objects were calculated before and we can limit ourselves to make use of the results.For the case of two parallel conducting walls separated by a fixed distance a we have [3,4] E i (r, t)E j (r, t) 0 = …”

mentioning

confidence: 99%

“…The electromagnetic field correlators for the case of two parallel perfectly conducting surfaces separated by a distance a were evaluated in [3] and in [4]. For the case of a perfectly conducting plane wall and a perfectly permeable plane wall, a setup first introduced by Boyer [5], they were calculated in [4]. These mathematical objects, closely related to the pertinent electromagnetic Green's functions, were also employed to obtain an alternative view of the Casimir effect [6] through the quantum version of the Lorentz force between the walls [7].…”

mentioning

confidence: 99%

See 2 more Smart Citations

Casimir-Polder interaction in the presence of parallel walls

Santos¹,

Sobrinho²,

Tort³

2005

Braz. J. Phys.

View full text Add to dashboard Cite

Making use of the quantum correlators associated with the Maxwell field vacuum distorted by the presence of plane parallel material surfaces we rederive the Casimir-Polder interaction in the presence of plane parallel conducting walls. For a configuration consisting of a conducting wall and a magnetically permeable one new results for the Casimir-Polder interaction potential are obtained.In 1948, Casimir and Polder [1] taking into account a suggestion made by experimentalists evaluated the interaction potential between two eletrical polarizable molecules separated by a distance r including the effects due to the finiteness of the speed of propagation of the electromagnetic interaction, i.e.: of the retardment. Casimir and Polder showed that the retardment causes the interaction potential to change from a r −6 power law to a r −7 power law. In the same paper, Casimir and Polder also analyzed the retarded interaction between an atom and a conducting wall and showed that the interaction potential in this case varies according to a r −4 power law, where now r is the distance between the atom and the wall. For an introduction to these subjects see [2]. Here we wish to show how it is possible with the help of the so called renormalized electromagnetic field correlators, in our case the ones that take into account the presence of the boundary conditions imposed on the fields, to reobtain the piece of Casimir and Polder's result for the atom-wall interaction that depends on the distortion of the vacuum oscillations of the electromagnetic field caused by the presence of parallel walls. The electromagnetic field correlators for the case of two parallel perfectly conducting surfaces separated by a distance a were evaluated in [3] and in [4]. For the case of a perfectly conducting plane wall and a perfectly permeable plane wall, a setup first introduced by Boyer [5], they were calculated in [4]. These mathematical objects, closely related to the pertinent electromagnetic Green's functions, were also employed to obtain an alternative view of the Casimir effect [6] through the quantum version of the Lorentz force between the walls [7].Let us first recall some aspects concerning electrically and magnetically polarizable bodies [8]. From a classical point of view the induced eletrical polarization density P can be thought of as a function of the electric and magnetic fields E and B. In many cases only the dependence on the eletric field is relevant. It can be shown that under conditions for which the effects of the retardment (i.e., of the finiteness of the speed of light) must be taken into account it suffices to consider the static eletrical polarizability α (0) only, see for instance [2] and references therein. If the electric field changes by δE, the interaction between the polarizable body and the electric field will change according to δV = −P [E] · δE = −α (0) E·δE. Therefore, if the field changes from zero to a finite value E, the interaction energy is V E = −α (0) E 2 /2. In the quantum version of this interaction pote...

show abstract

Magnetic permeability of constrained scalar QED vacuum

et al. 2000

Self Cite

View full text Add to dashboard Cite

We compute the influence of boundary conditions on the Euler-Heisenberg effective Lagrangian scalar QED scalar for the case of a pure magnetic field. The boundary conditions constrain the quantum scalar field to vanish on two parallel planes separeted by a distance a and the magnetic field is assumed to be constant, uniform and perpendicular to the planes. The effective Lagrangian is obtained using Schwinger's proper-time representation and exhibits new contributions generated by the boundary condition much in the same way as a material pressed between two plates exhibits new magnetic properties. The confined bosonic vacuum presents the expected diamagnetic properties and besides the new non-linear a-dependent contributions to the susceptibility we show that there exists also a new a-dependent contribution for the vacuum permeability in the linear approximation. *

show abstract

QED vacuum between a conducting and a permeable plate

Cited by 24 publications

References 29 publications

Electromagnetic field correlators, Maxwell stress tensor, and the Casimir effect for parallel walls

Electromagnetic field correlators, Maxwell stress tensor, and the Casimir effect for parallel walls

Casimir-Polder interaction in the presence of parallel walls

Magnetic permeability of constrained scalar QED vacuum

Contact Info

Product

Resources

About