| dc.description.abstract | We study thoroughly Casimir energy and Casimir
force in a rectangular cavity and piston with various boundary
conditions, for both scalar field and electromagnetic (EM) field.
Using the cylinder kernel approach, we find the Casimir energy
exactly and analyze the Casimir energy and Casimir force from the
point of view of closed classical paths (or optical paths). For the
scalar field, we study the rectangular cavity and rectangular piston
with all Dirichlet conditions and all Neumann boundary conditions
and then generalize to more general cases with any combination of
Dirichlet and Neumann boundary conditions. For the EM field, we
first represent the EM field by 2 scalar fields (Hertz potentials),
then relate the EM problem to corresponding scalar problems. We
study the case with all conducting boundary conditions and then
replace some conducting boundary conditions by permeable boundary
conditions. By classifying the closed classical paths into 4 kinds:
Periodic, Side, Edge and Corner paths, we can see the role played by
each kind of path. A general treatment of any combination of
boundary conditions is provided. Comparing the differences between
different kinds of boundary conditions and exploring the relation
between corresponding EM and scalar problems, we can understand the
effect of each kind of boundary condition and contribution of each
kind of classical path more clearly. | en |
