Physics – Quantum Physics
Scientific paper
2009-11-17
J.Phys.A43:015402,2010
Physics
Quantum Physics
9 pages, to appear in J. Phys. A: Math. Theor
Scientific paper
10.1088/1751-8113/43/1/015402
We show that in the presence of free charge carriers the definition of the frequency-dependent dielectric permittivity requires additional regularization. As an example, the dielectric permittivity of the Drude model is considered and its time-dependent counterpart is derived and analyzed. The respective electric displacement cannot be represented in terms of the standard Fourier integral. The regularization procedure allowing to circumvent these difficulties is suggested. For purpose of comparison it is shown that the frequency-dependent dielectric permittivity of insulators satisfies all rigorous mathematical criteria. This permits us to conclude that in the presence of free charge carriers the concept of dielectric permittivity is not as well defined as for insulators and we make a link to widely discussed puzzles in the theory of thermal Casimir force which might be caused by the use of such kind permittivities.
Bordag Michael
Geyer Bodo
Klimchitskaya Galina L.
Mostepanenko V. M.
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