Milton, Kimball A2019-04-272019-04-272010https://hdl.handle.net/11244/319142Recently the Casimir effect has been getting more popular because ofits importance in designing micro and nano scale machines. Working inthe language of quantum field theory simplified formulas for theCasimir energy for a massless scalar field are worked out. Theseformulas are applied to planar potentials and potentials in theannular region between two co-axial cylinders. A scalar equivalent tothe Lifshitz formula is applied to new cases of non-trivial planarpotentials, specifically two interacting linear potentials and twointeracting quadratic potentials. In addition many exact expressionsfor the Casimir energy between two weakly coupled objects are workedout for many non-trivial geometries. Exact closed form results are shownfor parallel cylinders, spheres, and finite ribbons and plates. Theseclosed form results are used to check the range of validity of theproximity force approximation.94 pagesapplication.pdfCasimir effecttext