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 Sfz. We study the cases with Td×Sfz and Sfz as the extra-dimensional spaces, where Td 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 MD. 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.
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