After a review of the standard calculation of the Casimir force between two
metallic plates at zero and non-zero temperatures, we present the study of
microscopic models to determine the large-distance asymptotic force in the
high-temperature regime. Casimir's conducting plates are modelized by plasmas
of interacting charges at temperature T. The charges are either classical, or
quantum-mechanical and coupled to a (classical) radiation field. In these
models, the force obtained is twice weaker than that arising from standard
treatments neglecting the microscopic charge fluctutations inside the bodies.
The enforcement of inert boundary conditions on the field in the usual
calculations turns out to be inadequate in this regime.
Other aspects of dispersion forces are also reviewed. The status of
(non-retarded) van der Waals-London forces in a dilute medium of non-zero
temperature and density is investigated. In a proper scaling regime called the
atomic limit (high dilution and low temperature), one is able to give the exact
large-distance atomic correlations up to exponentially small terms as T->0.
Retarded van der Waals forces and forces between dielectric bodies are also
reviewed.
Finally, the Casimir effect in critical phenomena is addressed by considering
the free Bose gas. It is shown that the grand-canonical potential of the gas in
a slab at the critical value of the chemical potential has finite size
corrections of the standard Casimir type. They can be attributed to the
existence of long-range order generated by gapless excitations in the phase
with broken continuous symmetry.Comment: Lecture notes prepared for the proceedings of the 1st Warsaw School
of Statistical Physics, Kazimierz, Poland, June 2005. To appear in Acta
Physica Polonica (2006). 52 pages, 0 figures. Available at
http://th-www.if.uj.edu.pl/acta/vol37/pdf/v37p2503.pd
