Kaluza-Klein pistons with noncommutative extra dimensions

2009/05/10 by V. K. Oikonomou
Physics and Astronomy · #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #Quantum Electrodynamics and Casimir Effect #hep-ph #hep-th

paper · pdf · doi:10.1007/s11232-011-0027-9

published as Theor.Math.Phys.166:337-355,2011 · 22 pages

arxiv created 2009/05/10 · openalex publication_date 2011/03/01 · arxiv updated 2011/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

We calculate the scalar Casimir energy and Casimir force for a R³× N Kaluza-Klein piston setup in which the extra dimensional space N contains a non-commutative 2-sphere, S_FZ. The cases to be studied are T^d× S_FZ and S_FZ respectively as extra dimensional spaces, with T^d the d dimensional commutative torus. The validity of the results and the regularization that the piston setup offers are examined in both cases. Finally we examine the 1-loop corrected Casimir energy for one piston chamber, due to the self interacting scalar field in the non-commutative geometry. The computation is done within some approximations. We compare this case for the same calculation done in Minkowski spacetime M^D. A discussion on the stabilization of the extra dimensional space within the piston setup follows at the end of the article.

Citations

• The Casimir force on a piston in the spacetime with extra compactified dimensions
• Casimir force on a piston
• New Developments in the Casimir Effect
• Quantum field theories with compact noncommutative extra dimensions