Simple Models of the Casimir Effect

AbstractThis chapter discusses several basic ideas and methods related to the calculation of the Casimir energies and forces using some simple models. The simplicity of these models means that cumbersome mathematical calculations can be avoided and they demonstrate the basic problems that will be repeatedly considered in the following chapters in a more sophisticated context. Important procedures such as regularization and renormalization of infinite quantities are illustrated, both physically and mathematically. Despite the elementary character of the chapter, the main physical situations where the Casimir effect arises (i.e., in regions with boundaries and in spaces with nontrivial topology) are discussed. Local and global approaches to the Casimir effect, and well-known formulas for the electromagnetic Casimir pressure and energy per unit area between two parallel ideal-metal planes are derived.