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Abstract
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In this research, a general formula for the Casimir force between ideal metal plate and a dissipative dielectric slab has been obtained. The dielectric function of the slab is
assumed to be an arbitrary complex function of frequency satisfying Kramers–Kronig relations. A classical expression for the radiation pressure of the vacuum fields on the slab is presented by using the Maxwell stress tensor. With the ransition to the quantum domain and using the fluctuation dissipation theorem and Kubo’s formula, the resulting
expression is written in terms of the imaginary part of the vector potential Green functions components of the system. Finally, by computing the Green function, the Casimir
force on the slab is obtained. This formalism enables us to calculate the Casimir force without resorting to the explicit form of the field operators. The general expression is
confirmed by limiting and comparing with one of the previous works.
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