# Towards quantum field theory on spacetimes with boundaries

December 22, 2015

Algebraic quantization has been applied on the class of globally hyperbolic
spacetime for many decades, leading to remarkable results. Nonetheless, the
presence of a boundary calls for a separate treatment, since, in general, it
breaks global hyperbolicity and it requires the introduction of boundary
conditions to the field equation. Although a general theory for such situations
is lacking, we develop an explicit construction of the algebraic quantization
of a massless scalar field on two prototypical geometries, by exploiting the
method of images. This well known technique gives a way to relate solutions of
the boundary value problem to solution of the field equation on Minkowski
spacetime, filling the gap with the standard theory. At the same time, we point
out some limits of reliability of this scheme.

Keywords:

algebraic quantum field theory, Casimir effect, boundary conditions