Vacuum Effects in the Presence of Walls

Casimir effects have for many years been the subject of painstaking experiments and a variety of theoretical techniques, but it is only recently that they have attracted widespread attention. The surge of interest is attributable in large part to experimental developments. To the list of subtler reasons I would add one that can best be appreciated by the cognoscenti: Larry’s lapidary elucidations of nearly every aspect of Casimir forces. I would also list a more personal if less important influence: some of us, before Casimir effects went mainstream, found encouragement in the fact that we could count Larry Spruch among the workers in the field. The effect of walls is to impose boundary conditions on the electromagnetic field and thereby to modify its spectral properties. Thus, for example, the Lamb shift associated with vacuum field fluctuations in free space is modified in a way that depends on the position of the atom with respect to any walls. For an atom at a (large) distance d from a perfectly conducting wall, the position-dependent level shift is given by the Casimir-Polder formula: E(d) = −3αh̄c/8πd, where α is the static polarizability. For two parallel conducting walls in otherwise empty space the modification of the vacuum field leads to an attractive force between the walls given by the Casimir formula: F = −πh̄c/240d per unit area, where d is the wall separation. Both effects have in recent years been unambiguously demonstrated. Three excellent reviews of these and other Casimir effects are available ( [1][3]). Another wall effect occurs when the atom in the Casimir-Polder problem is replaced by an electron which, as a consequence of its electrostatic interaction with its image, can have a bound-state spectrum resembling that of a one-dimensional hydrogen atom. Shakeshaft and Spruch [4] showed that the electron experiences a level shift interpretable