PHYSICS SEMINAR
TOPOLOGICAL CASIMIR EFFECT IN A KALUZA-KLEIN SPACETIME
Dr. Ariel Edery
Physics Department
Bishop's University
Friday, February 5, 2010
1:30 pm
Nicolls 1
We calculate the effect of an extra compact dimension on the Casimir force between perfectly conducting parallel plates where the extra dimension is compactified on a circle of radius R (an M4 x S1 spacetime known as a Kaluza-Klein spacetime). Our starting point is the Kaluza Klein decomposition of the 5D Maxwell action into a massless sector containing the 4D Maxwell action together with an extra massless scalar field and a Proca sector containing 4D gauge fields with masses mn = n/R where n is a positive integer. An important point is that in the presence of perfectly conducting parallel plates, the three polarizations of the photon do not yield three discrete (reflected) modes but two discrete modes and one continuum (penetrating) mode. The perfect conductors become partially transparent due to the topology of the spacetime. The massless sector reproduces Casimir’s original result and the Proca sector yields the corrections. The contribution from the Proca continuum mode is obtained within the framework of Lifshitz theory for plane parallel dielectrics whereas the discrete modes are calculated via novel 5D formulas for the piston geometry. An interesting physical manifestation of the extra compact dimension is that the Casimir force between the conducting plates depends on the thicknesses of the slabs.
