Casimir effect on the radius stabilization of the noncommutative torus

Huang, Wung-Hong

doi:10.1016/s0370-2693(00)01352-6

Cited by 26 publications

(20 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this letter, we are interested in studying the Casimir effect in the presence of extra compactified dimensions. The research on Casimir effect in the scenarios with extra dimensions have been studied in the context of string theory [26,27,28,29], dark energy and cosmological constant [16,17,18,19,21,22,25,30,31,32,33,34,35,36,37], as well as stabilization of extra dimensions [23,24,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53]. Casimir force for massless scalar field with Dirichlet boundary conditions on a pair of parallel plates inside space with extra dimensions compactified to a torus T n = (S 1 ) n have been calculated in [54,55,56,57,58,59].…”

mentioning

confidence: 99%

Finite temperature Casimir effect in spacetime with extra compactified dimensions

Teo

2009

Physics Letters B

View full text Add to dashboard Cite

In this letter, we derive the explicit exact formulas for the finite temperature Casimir force acting on a pair of parallel plates in the presence of extra compactified dimensions within the framework of Kaluza-Klein theory. Using the piston analysis, we show that at any temperature, the Casimir force is always attractive and the effect of extra dimensions becomes stronger when the size or number of the extra dimensions increases. These properties are not affected by the explicit geometry and topology of the Kaluza-Klein space. Theories with extra space dimensions can be dated back to the work of Kaluza and Klein [1,2] in an attempt to unify gravity and classical electrodynamics. The advent of string theory has made the idea of extra dimensions indispensable [3]. Recently, the interest for physical models that contain extra warped dimensions come from the endeavor to explain the large gap between the Planck and electroweak scale (the hierarchy problem), and the dark energy and cosmological constant problem [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25]. In this letter, we are interested in studying the Casimir effect in the presence of extra compactified dimensions. The research on Casimir effect in the scenarios with extra dimensions have been studied in the context of string theory [26,27,28,29], dark energy and cosmological constant [16,17,18,19,21,22,25,30,31,32,33,34,35,36,37], as well as stabilization of extra dimensions [23,24,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53]. Casimir force for massless scalar field with Dirichlet boundary conditions on a pair of parallel plates inside space with extra dimensions compactified to a torus T n = (S 1 ) n have been calculated in [54,55,56,57,58,59]. The dependence of the Casimir energy on a cut-off scale was investigated in [25]. Casimir effect for electromagnetic fields confined between a pair of parallel and perfectly conducting plates in R d+1 was considered in [60]. In the case the extra dimension is compactified to a circle S 1 , it was studied in [25,61,62,63]. For the Randall-Sundrum spacetime model, the Casimir force due to massless scalar fields subject to Dirichlet boundary conditions on two parallel plates were calculated in [64,65,66].Despite the importance of the thermal corrections, most of the works mentioned above dealt with Casimir effect at zero temperature. In particular, we would like to mention the two papers by Cheng [56,58] where he calculated the Casimir force acting on a pair of parallel plates due to massless scalar field with Dirichlet boundary conditions in spacetime with n extra dimensions compactified to a torus. As pointed out in the comment [59], the earlier paper [56] concluded that the presence of extra dimensions will give rise to repulsive Casimir force under certain conditions. However, this result was invalidated by the author himself in the later paper [58], where he redid the calculations in a more physical setup known as piston [67] and concluded that the Casimir force shall always be attractive. The fini...

show abstract

mentioning

confidence: 99%

Finite temperature Casimir effect in spacetime with extra compactified dimensions

Teo

2009

Physics Letters B

View full text Add to dashboard Cite

show abstract

“…• The question how vacuum fluctuations affect the * Electronic address: katjap@th.physik.uni-frankfurt.de stability of extra dimensions has been explored in [16,17,18,19,20,21]. Especially the detailed studies in the Randall-Sundrum model have shown the major contribution of the Casimir effect to stabilise the radion [22,23,24,25].…”

mentioning

confidence: 99%

The Casimir effect in the presence of compactified universal extra dimensions

et al. 2004

View full text Add to dashboard Cite

“…On the one hand, it has been investigated as a candidate for the dark energy that accounts for the accelerated expansion of the Universe [3][4][5][6][7][8][9]. On the other hand, it was studied for its role in the stabilization mechanism of extra dimensions [10][11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Electromagnetic Casimir piston in higher-dimensional spacetimes

Teo

2011

Phys. Rev. D

View full text Add to dashboard Cite

We consider the Casimir effect of the electromagnetic field in a higher-dimensional spacetime of the form M Â N , where M is the four-dimensional Minkowski spacetime and N is an n-dimensional compact manifold. The Casimir force acting on a planar piston that can move freely inside a closed cylinder is investigated. Different combinations of perfectly conducting boundary conditions and infinitely permeable boundary conditions are imposed on the cylinder and the piston. It is verified that if the piston and the cylinder have the same boundary conditions, the piston is always going to be pulled towards the closer end of the cylinder. However, if the piston and the cylinder have different boundary conditions, the piston is always going to be pushed to the middle of the cylinder. By taking the limit where one end of the cylinder tends to infinity, one obtains the Casimir force acting between two parallel plates inside an infinitely long cylinder. The asymptotic behavior of this Casimir force in the high temperature regime and the low temperature regime are investigated for the case where the cross section of the cylinder in M is large. It is found that if the separation between the plates is much smaller than the size of N , the leading term of the Casimir force is the same as the Casimir force on a pair of large parallel plates in the (4 þ n)-dimensional Minkowski spacetime. However, if the size of N is much smaller than the separation between the plates, the leading term of the Casimir force is 1 þ h=2 times the Casimir force on a pair of large parallel plates in the four-dimensional Minkowski spacetime, where h is the first Betti number of N . In the limit the manifold N vanishes, one does not obtain the Casimir force in the fourdimensional Minkowski spacetime if h is nonzero. Therefore the data obtained from Casimir experiments suggest that the first Betti number of the extra dimensions should be zero.

show abstract

Casimir effect on the radius stabilization of the noncommutative torus

Abstract: We evaluate the one-loop correction to the spectrum of Kaluza-Klein system for the φ

Cited by 26 publications

References 16 publications

Finite temperature Casimir effect in spacetime with extra compactified dimensions

Finite temperature Casimir effect in spacetime with extra compactified dimensions

The Casimir effect in the presence of compactified universal extra dimensions

Electromagnetic Casimir piston in higher-dimensional spacetimes

Contact Info

Product

Resources

About