Abstract:
 In recent years, great breakthroughs have been achieved in computing the Casimir interaction energy between two compact objects. Using path integral and the theory of multiple scattering, it was shown that the Casimir energy can be expressed in terms of a functional determinant, which is referred to as the TGTG formula. The T matrices are related to the scattering matrices and the G matrices are the translation matrices. In this talk, we discuss how to derive the TGTG formula using the mode summation approach, which do not rely on the theory of path integral and multiple scattering. Explicit prescriptions for computing the T and G matrices are given, and an explicit example will be discussed.
