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TMF, 2011, Volume 166, Number 3, Pages 388–409 (Mi tmf6618)  

This article is cited in 3 scientific papers (total in 3 papers)

Kaluza–Klein pistons with noncommutative extra dimensions

V. K. Oikonomouab

a Department of Theoretical Physics, Aristotle University of Thessaloniki, Thessaloniki, Greece
b Technological Education Institute of Serres, Serres, Greece

Abstract: 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 $S_fz$. We study the cases with $T^d\times S_fz$ and $S_fz$ 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, Casimir force, noncommutative geometry, piston, extra dimension

DOI: https://doi.org/10.4213/tmf6618

Full text: PDF file (451 kB)
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English version:
Theoretical and Mathematical Physics, 2011, 166:3, 337–355

Bibliographic databases:

Document Type: Article
Received: 06.03.2010
Revised: 28.06.2010

Citation: V. K. Oikonomou, “Kaluza–Klein pistons with noncommutative extra dimensions”, TMF, 166:3 (2011), 388–409; Theoret. and Math. Phys., 166:3 (2011), 337–355

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. K. Oikonomou, “Casimir force of fermions coupled to monopoles in six-dimensional spacetime”, Int. J. Geom. Methods Mod. Phys., 11:1 (2014), 1450011, 23 pp.  crossref  mathscinet  zmath  isi  scopus
    2. Zhai X.-H. Lin R.-H. Feng Ch.-J. Li X.-Zh., “Some Developments of the Casimir Effect in P-Cavity of (D+1)-Dimensional Space-Time”, Int. J. Mod. Phys. A, 29:30 (2014), 1430068  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. Khanna F.C., Malbouisson A.P.C., Malbouisson J.M.C., Santana A.E., “Quantum Field Theory on Toroidal Topology: Algebraic Structure and Applications”, Phys. Rep.-Rev. Sec. Phys. Lett., 539:3 (2014), 135–224  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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