Compact dimensions and the Casimir effect: the Proca connection

Edery, Ariel; Marachevsky, Valery N.

doi:10.1088/1126-6708/2008/12/035

Cited by 46 publications

(46 citation statements)

References 36 publications

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“…Extra-dimensional theories with low-energy compactification scale predict Yukawa-type corrections to Newton's gravitational law and the measurements of the Casimir forces between macroscopic bodies provide a sensitive test for constraining the parameters of the corresponding long-range interactions [28][29][30][31][32]. The influence of extra compactified dimensions on the Casimir effect in the classical configuration of two parallel plates has been recently discussed for scalar [33][34][35][36][37][38][39][40], electromagnetic [41][42][43][44][45] and fermionic [46][47][48] fields.…”

Section: Introductionmentioning

confidence: 99%

Casimir effect for scalar current densities in topologically nontrivial spaces

2015

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We evaluate the Hadamard function and the vacuum expectation value (VEV) of the current density for a charged scalar field, induced by flat boundaries in spacetimes with an arbitrary number of toroidally compactified spatial dimensions. The field operator obeys the Robin conditions on the boundaries and quasiperiodicity conditions with general phases along compact dimensions. In addition, the presence of a constant gauge field is assumed. The latter induces Aharonov-Bohm-type effect on the VEVs. There is a region in the space of the parameters in Robin boundary conditions where the vacuum state becomes unstable. The stability condition depends on the lengths of compact dimensions and is less restrictive than that for background with trivial topology. The vacuum current density is a periodic function of the magnetic flux, enclosed by compact dimensions, with the period equal to the flux quantum. It is explicitly decomposed into the boundary-free and boundary-induced contributions. In sharp contrast to the VEVs of the field squared and the energy-momentum tensor, the current density does not contain surface divergences. Moreover, for Dirichlet condition it vanishes on the boundaries. The normal derivative of the current density on the boundaries vanish for both Dirichlet and Neumann conditions and is nonzero for general Robin conditions. When the separation between the plates is smaller than other length scales, the behavior of the current density is essentially different for non-Neumann and Neumann boundary conditions. In the former case, the total current density in the region between the plates tends to zero. For Neumann boundary condition on both plates, the current density is dominated by the interference part and is inversely proportional to the separation. a

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Section: Introductionmentioning

confidence: 99%

Casimir effect for scalar current densities in topologically nontrivial spaces

2015

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“…The quite vast current literature of Casimir interactions in relation to a massive photon discusses only the standard Casimir effect in the geometry of two parallel conductor plates. This had been studied in the pioneering work of Barton and Dombey [20,21] and subsequently taken up by several authors in other BSM scenarios [28][29][30][31][32][33][34][35][37][38][39][40][41], but always considering the Casimir effect between parallel plates.…”

Section: Discussionmentioning

confidence: 99%

“…By substituting (41) in (34), differentiating and performing the appropriate change of variables one obtains the following expression:…”

Section: B Casimir -Polder Interaction For Massive Photonsmentioning

confidence: 99%

“…The Casimir effect has also been investigated in extended theories of gravity [37,38] and Post-Newtonian gravity with Lorentz-violation [39]. The Casimir force for parallel plates in the spacetime with one extra space-like dimension is computed in terms of the decomposition into a Kaluza-Klein (KK) tower of massive vector fields in [40,41].…”

Section: Introductionmentioning

confidence: 99%

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Casimir-Polder interactions with massive photons: Implications for BSM physics

Mattioli¹,

Frassino²,

Panella³

2019

Phys. Rev. D

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We present the derivation of the Casimir-Polder interactions mediated by a massive photon between two neutral systems described in terms of their atomic polarizability tensors. We find a compact expression for the leading term at large distances between the two systems. Our result reduces, in the mass-less photon limit, to the standard Casimir-Polder. We discuss implications of our findings with respect to recent scenarios of physics beyond the standard model such as universal extra dimensions, Randall-Sundrum and scale-invariant models. For each model we compute the correction to the Casimir-Polder interaction in terms of the free parameters.

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“…In the spacetime with one additional dimension compactified to a circle of radius R, the Casimir force for an electromagnetic field between two perfectly conducting parallel plates was also explored and it was shown that there are two reflecting (discrete) modes and one penetrating (continuum) mode propagating through the conductor. It is found that they recover standard Casimir result in the limit as the radius tends to vanish [28]. The UV cut-off dependence of the Casimir energy for perfect conductors with an extra compact dimension was also studied recently and the constraints from Casimir effect experiments on the vacuum energy, the cosmological constant and compact extra dimensions was obtained [29].…”

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confidence: 90%

Casimir Force on a Piston in Randall–Sundrum Models

Cheng¹

2010

Commun. Theor. Phys.

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The Casimir effect of a piston for massless scalar fields which satisfy Dirichlet boundary conditions in the context of five-dimensional Randall-Sundrum models is studied. In these scenarios we derive and calculate the expression for the Casimir force on the piston. We also discuss the Casimir force in the limit that one outer plate is moved to the remote place to show that the nature of the reduced force between the parallel plates left. In the Randall-Sundrum model involving two branes the two plates attract each other when they locate very close, but the reduced Casimir force turns to be repulsive as the plates separation is not extremely tiny, which is against the experimental phenomena. In the case of one brane model the shape of the reduced Casimir force is similar to that of the standard two-parallel-system in the four-dimensional flat spacetimes while the sign of force remains negative.

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Compact dimensions and the Casimir effect: the Proca connection

Cited by 46 publications

References 36 publications

Casimir effect for scalar current densities in topologically nontrivial spaces

Casimir effect for scalar current densities in topologically nontrivial spaces

Casimir-Polder interactions with massive photons: Implications for BSM physics

Casimir Force on a Piston in Randall–Sundrum Models

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