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Description:
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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 ,â  )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 . |