  In this master thesis a configuration space method presented by C. Dullemond
and E. van Beveren for computing all propagators of a scalar field (Wightman,
Hadamard and Schwinger functions,retarded, advanced and Feynman propagator) is
reviewed for four-dimensional Minkowski and Anti de Sitter spacetime AdS_4.
This method is then applied for AdS_d as well as de Sitter spacetime dS_d of
arbitrary dimension d, obtaining results in agreement with the literature. The
advantages of the method are that it needs neither mode summation nor analytic
continuation from euclidean time, while delivering the propagators above
including (i-epsilon)-prescription, plus as a nice bonus the conformal
dimension of a corresponding CFT field. General properties of the considered
spacetimes (namely various coordinate systems and their metrics, chordal
distances, relations between conformal dimensions \Delta and the mass m of the
scalar field, geodesics and the invariance of time ordering) are also examined
and compiled from various sources, providing an overview of geometrical
properties of AdS and dS spacetimes.
