|M.Sc Student||Rubin Shimon|
|Department||Department of Physics||Supervisors||Professor Ady Mann|
|Dr. Joshua Feinberg|
|Professor Emeritus Michael Revzen|
In this work we investigate the energy, free energy and entropy of the scalar massless field in vacuum under Dirichlet and Neumann boundary conditions (b.c.) on two parallel hyperplanes in N spatial dimensions. We shall assume throughout the simplifying assumption that all the modes of the scalar field are subjected to the b.c., as if the hyperplanes are ideal conductors or ideal permeable materials. The ground state energy (free energy) is the sum over the zero point energies (free energies) contributed by modes of the scalar field. We define the Casimir energy (free energy) as the difference of the sum of the energies (free energies) of the constrained modes and the sum of energies (free energies) of all the free modes. Casimir force is attractive in the case of Dirichlet-Dirichlet b.c. and repulsive in the case of Dirichlet-Neumann b.c. for all temperatures and separations. We study the high temperature limit in which Casimir energy tends to zero and Casimir free energy is linear function of the temperature. Casimir force in that limit is determined only by the Casimir entropy (purely “entropic”). Calculations at zero temperature were performed by two methods. Mode summation method (for all N, for the cases Dirichlet-Dirichlet and Dirichlet-Neumann b.c.) and, for comparison, Green's function method (for all N, for the cases of Dirichlet-Dirichlet, Dirichlet-Neumann and Neumann-Neumann b.c.); they coincide and agree with the previous results.