Geodesic
Kaluza–Klein pistons with noncommutative extra dimensions
Teoretičeskaâ i matematičeskaâ fizika, Tome 166 (2011) no. 3, pp. 388-409 Cet article a éte moissonné depuis la source Math-Net.Ru

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We calculate the scalar Casimir energy and Casimir force for an $\mathbb R^3{\times}N$ Kaluza–Klein piston setup in which the extra-dimensional space $N$ contains a noncommutative two-dimensional sphere $S_\text{fz}$. We study the cases with $T^d\times S_\text{fz}$ and $S_\text{fz}$ as the extra-dimensional spaces, where $T^d$ is the $d$-dimensional commutative torus, and examine the validity of the results and the regularization obtained in the piston setup in each case. We examine the Casimir energy with one-loop corrections for one piston chamber due to the self-interacting scalar field in the noncommutative geometry. We compute with some approximations. We compare the obtained results with the results of analogous computations for the Minkowski space–time $M^D$. In conclusion, we discuss the stabilization of the extra-dimensional space in the piston setup.
Keywords: Casimir energy, noncommutative geometry, piston
Mots-clés : Casimir force, extra dimension. 
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     author = {V. K. Oikonomou},
     title = {Kaluza{\textendash}Klein pistons with noncommutative extra dimensions},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2011_166_3_a4/}
}
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V. K. Oikonomou. Kaluza–Klein pistons with noncommutative extra dimensions. Teoretičeskaâ i matematičeskaâ fizika, Tome 166 (2011) no. 3, pp. 388-409. http://geodesic.mathdoc.fr/item/TMF_2011_166_3_a4/

[1] K. Kirsten, S. A. Fulling, Phys. Rev. D, 79:6 (2009), 065019, 10 pp., arXiv: 0901.1902 | DOI | MR

[2] E. Elizalde, S. D. Odintsov, A. A. Saharian, Phys. Rev. D, 79:6 (2009), 065023, 13 pp., arXiv: 0902.0717 | DOI | MR

[3] S. A. Fulling, K. Kirsten, Rhys. Rev. Lett. B, 671:1 (2009), 179–180, arXiv: 0811.0779 | DOI

[4] A. Edery, Phys. Rev. D, 75:10 (2007), 105012, 9 pp., arXiv: ; J. Phys. A, 39:3 (2006), 685–712, arXiv: ; A. Edery, V. Marachevsky, Phys. Rev. D, 78:2 (2008), 025021, 10 pp., arXiv: ; A. Edery, I. MacDonald, JHEP, 09 (2007), 005, 27 pp., arXiv: hep-th/0610173math-ph/05100560805.40380708.0392 | DOI | DOI | MR | Zbl | DOI | DOI

[5] R. M. Cavalcanti, Phys. Rev. D, 69:6 (2004), 065015, 5 pp., arXiv: quant-ph/0310184 | DOI

[6] V. K. Oikonomou, Modern Phys. Lett. A, 24:30 (2009), 2405–2423, arXiv: 0903.4159 | DOI | MR

[7] L. P. Teo, Phys. Lett. B, 672:2 (2009), 190–195, arXiv: 0812.4641 | DOI | MR

[8] S. C. Lim, L. P. Teo, Ann. Phys., 324:8 (2009), 1676–1690, arXiv: 0807.3613 | DOI | Zbl

[9] H. Cheng, Rhys. Rev. Lett. B, 668:1 (2008), 72–77, arXiv: 0801.2810 | DOI

[10] H. B. G. Casimir, Proc. Akad. Wet. Amsterdam, 51 (1948), 793–795 | MR | Zbl

[11] S. A. Fulling, J. H. Wilson, Repulsive Casimir pistons, arXiv: quant-ph/0608122

[12] W.-H. Huang, JHEP, 11 (2000), 041, 13 pp., arXiv: ; 07 (2002), 064, 13 pp., arXiv: hep-th/0011037hep-th/0203051 | DOI | MR | Zbl | DOI | MR

[13] R. J. Szabo, Phys. Rep., 378:4 (2003), 207–299, arXiv: hep-th/0109162 | DOI | MR | Zbl

[14] A. A. Bytsenko, E. Elizalde, S. Zerbini, Phys. Rev. D, 64:10 (2001), 105024, 7 pp., arXiv: ; E. Elizalde, Comm. Math. Phys., 198:1 (1998), 83–95, arXiv: ; J. Phys. A, 34:14 (2001), 3025–3035, arXiv: hep-th/0103128hep-th/9707257hep-th/0012154 | DOI | MR | DOI | MR | Zbl | DOI | MR | Zbl

[15] J. Gomis, T. Mehen, M. B. Wise, JHEP, 08 (2000), 029, 15 pp., arXiv: hep-th/0006160 | DOI | MR | Zbl

[16] M. Bordag, U. Mohideen, V. M. Mostepanenko, Phys. Rep., 353:1–3 (2001), 1–205, arXiv: quant-ph/0106045 | DOI | MR | Zbl

[17] X.-H. Zhai, X.-Z. Li, Phys. Rev. D, 76:4 (2007), 047704, 4 pp., arXiv: hep-th/0612155 | DOI

[18] V. N. Marachevsky, Phys. Rev. D, 75:8 (2007), 085019, 6 pp., arXiv: hep-th/0703158 | DOI

[19] L. Perivolaropoulos, Phys. Rev. D, 77:10 (2008), 107301, 4 pp., arXiv: 0802.1531 | DOI

[20] E. Elizalde, Ten Physical Applications of Spectral Zeta Functions, Lecture Notes in Phys. New Ser. m: Monogr., 35, Springer, Berlin, 1995 ; E. Elizalde, S. D. Odintsov, A. Romeo, A. A. Bytsenko, S. Zerbini, Zeta Regularization Techniques with Applications, World Sci., Singapore, 1994 | MR | Zbl | MR | Zbl

[21] K. Kirsten, Spectral Functions in Mathematics and Physics, Chapman Hall/CRC, Boca Raton, FL | MR | Zbl

[22] W.-H. Huang, Phys. Lett. B, 537:3–4 (2002), 311–320, arXiv: hep-th/0203176 | DOI | Zbl

[23] R. C. Myers, JHEP, 12 (1999), 022, 41 pp., arXiv: hep-th/9910053 | DOI | MR | Zbl

[24] S. Nam, JHEP, 10 (2000), 044, 10 pp., arXiv: hep-th/0008083 | DOI | Zbl

[25] T. Appelquist, A. Chodos, Phys. Rev. Lett., 50:3 (1983), 141–145 | DOI | MR

[26] H. Grosse, C. Klimčík, P. Prešnajder, Internat. J. Theoret. Phys., 35:2 (1996), 231–244 | DOI | MR | Zbl

[27] E. Elizalde, S. Nojiri, S. D. Odintsov, S. Ogushi, Phys. Rev. D, 67:6 (2003), 063515, 15 pp., arXiv: hep-th/0209242 | DOI | MR | Zbl

[28] K. Kirsten, J. Math. Phys., 35:1 (1994), 459–470 | DOI | MR | Zbl

[29] E. Elizalde, A. Romeo, Phys. Rev. D, 40:2 (1989), 436–443 ; J. Math. Phys., 30:5 (1989), 1133–1139 ; M. Bordag, E. Elizalde, K. Kirsten, S. Leseduarte, Phys. Rev. D, 56:8 (1997), 4896–4904, arXiv: ; M. Bordag, E. Elizalde, K. Kirsten, J. Math. Phys., 37:2 (1996), 895–916, arXiv: ; E. Elizalde, M. Bordag, K. Kirsten, J. Phys. A, 31:7 (1998), 1743–1759, arXiv: hep-th/9608071hep-th/9503023hep-th/9707083 | DOI | MR | DOI | MR | Zbl | DOI | MR | DOI | MR | Zbl | DOI | MR | Zbl

[30] K. Kirsten, J. Math. Phys., 32:11 (1991), 3008–3014 | DOI | MR | Zbl

[31] X.-H. Zhai, Y.-Y. Zhang, X.-Z. Li, Modern Phys. Lett. A, 24:5 (2009), 393–400, arXiv: 0808.0062 | DOI | Zbl