  In this article we discuss the interplay between causal structures of
symmetric spaces and geometric aspects of Algebraic Quantum Field Theory
(AQFT). The central focus is the set of Euler elements in a Lie algebra, i.e.,
elements whose adjoint action defines a 3-grading. In the first half of this
article we survey the classification of reductive causal symmetric spaces from
the perspective of Euler elements. This point of view is motivated by recent
applications in AQFT. In the second half we obtain several results that prepare
the exploration of the deeper connection between the structure of causal
symmetric spaces and AQFT. In particular, we explore the technique of strongly
orthogonal roots and corresponding systems of sl_2-subalgebras. Furthermore, we
exhibit real Matsuki crowns in the adjoint orbits of Euler elements and we
describe the group of connected components of the stabilizer group of Euler
elements.
