The Casimir Polder force on a small polarizable particle (a ``point'' particle) situated in a wedge-shaped cavity with perfectly conducting walls is calculated, at zero temperature. Various special cases are examined. In particular, agreement with the conventional Casimir Polder formula is obtained if the opening angle : of the wedge equals ?.
1998 Academic Press
I. INTRODUCTION
The fluctuating electromagnetic field in a wedge geometry is a very attractive system to study, both because the geometry makes it so simple to avoid in particular the intricacies of curved boundaries and, also, because it permits us to analyse some of the central issues in quantum field theory. The geometry is sketched in Fig. 1. The opening angle of the wedge is :. For simplicity we take the two surfaces %=0 and %=: to be perfectly conducting.
The present paper is a continuation of a previous work [1]. In that paper, the expectation values of the components of the electromagnetic energy-momentum tensor were calculated, within the framework of Schwinger's source theory [2]. We derived herefrom the Casimir surface force on the walls. Here, we shall calculate the attractive electromagnetic force on a neutral small polarizable particle ideally a point particle placed in the cavity. Our considerations are applicable for the case of ``large'' distances, r> >* 0 #2?cÂ| 0 , at which retardation effects have to be taken into account. Here * 0 denotes the wavelength associated with a typical absorption frequency in the material. As a reasonable choice we may take | 0 =3_10 16 s &1 (in the ultraviolet region), from which it follows that * 0 t50 nm. Thus our considerations hold when the distance r from the cusp (the origin) satisfies the inequality r> >50 nm. Actually if the angle : is small, this inequality can be replaced by Article No. PH985814 134 0003-4916Â98 25.00