Cylinder kernel expansion of Casimir energy with a Robin boundary
Abstract
We compute the Casimir energy of a massless scalar field obeying the Robin
boundary condition on one plate and the Dirichlet boundary condition on another plate for two parallel plates with a separation of alpha. The Casimir
energy densities for general dimensions (D = d + 1) are obtained as functions of alpha
and beta by studying the cylinder kernel. We construct an infinite-series solution as
a sum over classical paths. The multiple-reflection analysis continues to apply. We
show that finite Casimir energy can be obtained by subtracting from the total vacuum
energy of a single plate the vacuum energy in the region (0,âÂÂ)x R^d-1. In comparison
with the work of Romeo and Saharian(2002), the relation between Casimir energy and
the coeffcient beta agrees well.
Citation
Liu, Zhonghai (2006). Cylinder kernel expansion of Casimir energy with a Robin boundary. Master's thesis, Texas A&M University. Texas A&M University. Available electronically from https : / /hdl .handle .net /1969 .1 /4245.