### Problems with the Thermal Casimir Force Between
Real Metals

**Galina L. Klimchitskaya**

*Physics Department, Federal University of Paraiba,
C.P.5008,*

CEP 58059-970, Joao Pessoa, Pb-Brazil

(on leave from North-West Polytechnical University, St.Petersburg,
Russia)

The energy of fluctuation electromagnetic field is investigated
for the thermal Casimir force acting between parallel plates made
of real metal. It is proved that for nondissipative media with
temperature independent dielectric permittivity the energy at
nonzero temperature comprises of the (renormalized) energies of
the zero-point and thermal photons. If the dielectric permittivity
depends on temperature the energy contains additional terms proportional
to the derivatives of the dielectric permittivity with respect
to temperature, and the quasiparticle interpretation fails. Previous
computations of the Casimir energy in the framework of the Lifshitz
formula at zero temperature and optical tabulated data supplemented
by the Drude model at room temperature are analysed. It is demonstrated
that this quantity does not serve as a good approximation neither
to free energy nor to energy. The physical

interpretation of this hybrid quantity is suggested. The contradictory
results in the recent literature on whether or not the zero-frequency
term of the Lifshitz formula for the perpendicular polarized modes

contribute to physical quantities are discussed. Four main approaches
to the resolution of this problem are specified. The precise expressions
for entropy of the fluctuation field between plates made of real
metal are obtained and this helps to decide between different
approaches. The conclusion is that the Lifshitz formula supplemented
by the plasma model and the surface impedance approach are best
suited to describe the thermal Casimir force between real metals.