Kaluza-Klein pistons with noncommutative extra dimensions

摘要

We calculate the scalar Casimir energy and Casimir force for an ?3 × 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.