General approach to Casimir force problems based on local reflection amplitudes and Huygens' principle

In this paper we describe an approach to Casimir force problems that is ultimately generalizable to all fields, boundary conditions, and cavity geometries. This approach utilizes locally defined reflection amplitudes to express the energy per unit area of any Casimir interaction. To demonstrate this approach we solve a number of Casimir Force problems including the case of uniaxial boundary conditions in a parallel-plate cavity.