The Derjaguin approximation and its descendants

F.D. MAZZITELLI

Les Houches

Workshop; Casimir Physics 2014; 2014

CNRS-Francia

The proximity force approximation (PFA), introduced by Derjaguin many years ago, is widely used in different areas of physics to compute forces of different origin between close and gently curved surfaces. Until recently, the PFA was believed to be an uncontrolled approximation. In this talk, I will review recent works of our group, where we showed that PFA can be understood as the leading order approximation of a derivative expansion of the interaction energy, when the latter is regarded as a functional of the shape of the surfaces. Therefore, the PFA can be derived from first principles and improved using usual techniques of quantum field theory. I will discuss the conditions under which the corrections to the PFA are local functionals of the shapes, and present an unifed view of the different approximations used in Casimir, nuclear, and colloidal physics, all of them related with the original proposal by Derjaguin.