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Kaluza-Klein pistons with noncommutative extra dimensions

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Abstract

We calculate the scalar Casimir energy and Casimir force for an ℝ3 × 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×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.

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Authors and Affiliations

  1. Department of Theoretical Physics, Aristotle University of Thessaloniki, Thessaloniki, Greece

    V. K. Oikonomou

  2. Technological Education Institute of Serres, Serres, Greece

    V. K. Oikonomou

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  1. V. K. Oikonomou
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Correspondence to V. K. Oikonomou.

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Prepared from an English manuscript submitted by the author; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 166, No. 3, pp. 388–409, March, 2011.

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Oikonomou, V.K. Kaluza-Klein pistons with noncommutative extra dimensions. Theor Math Phys 166, 337–355 (2011). https://doi.org/10.1007/s11232-011-0027-9

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  • DOI: https://doi.org/10.1007/s11232-011-0027-9

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