Geodesic
Kaluza--Klein pistons with noncommutative extra dimensions
Teoretičeskaâ i matematičeskaâ fizika, Tome 166 (2011) no. 3, pp. 388-409

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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. 
@article{TMF_2011_166_3_a4,
     author = {V. K. Oikonomou},
     title = {Kaluza--Klein pistons with noncommutative extra dimensions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {388--409},
     publisher = {mathdoc},
     volume = {166},
     number = {3},
     year = {2011},
     language = {ru},
     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/