BOUNDARIES IMMERSED IN A SCALAR QUANTUM-FIELD

We study the interaction between a scalar quantum field <(phi)over cap >(x), and many different boundary configurations constructed from (par allel and orthogonal) thin planar surfaces on which <(phi)over cap>(x) is constrained to vanish, or to satisfy Neumann conditions. For most of these boundaries the Casimir problem has not previously been invest igated. We calculate the canonical and improved vacuum stress tensors [<(T-mu upsilon)over cap>(x)] and [<(Theta(mu upsilon))over cap>(x)] o f <(phi)over cap>(x) for each example. From these we obtain the local Casimir forces on all boundary planes. For massless fields, both vacuu m stress tensors yield identical attractive local Casimir forces in al l Dirichlet examples considered. This desirable outcome is not a prior i obvious, given the quite different features of [<(T-mu upsilon)over cap>(x)] and [<(Theta(mu upsilon))over cap>(x)]. For Neumann condition s, [<(T-mu upsilon)over cap>(x)] and [<(Theta(mu upsilon))over cap>(x) ] lead to attractive Casimir stresses which are not always the same. W e also consider Dirichlet and Neumann boundaries immersed in a common scalar quantum field, and find that these repel. The extensive catalog ue of worked examples presented here belongs to a large class of compl etely solvable Casimir problems. Casimir forces previously unknown are predicted, among them ones which might be measurable.