The Casimir force in the semi-classical regime : a microscopic theory

The present thesis is devoted to a detailed study of the Casimir force exerting between two parallel metallic plates whose conducting behaviour is described on the microscopic level. In the semi-classical regime, which corresponds to large separations and high temperatures, the theoretical value of this force – which exhibits a universal character – is subject to a controversy revolving around a factor 2. Current theories describe the plates macroscopically or semi-macroscopically and impose perfect boundary conditions to the field at their interface. In a statistical mechanical framework, we perform a direct calculation of the average force exerting between the fluctuating charges of a two-slab system in the semi-classical regime. In a first model, the charges are classical. The calculation is then generalised to quantum plasmas coupled to the radiation field, by means of path integral formalism. Relying on these accurate models, we can pronounce on the correct value of the force. In addition, we explain its universality as being the result of perfect screening mechanisms reflecting the effective shielding of the charges in the conductors. We conclude that although shielded, charge fluctuations inside the conductors cannot be neglected.