Configuration Space Methods and Time Ordering for Scalar Propagators in (Anti and) de Sitter Spacetimes
Abstract
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 AdS4. This method is then applied for AdSd as well as de Sitter spacetime dSd 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 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.
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