Configuration Space Methods and Time Ordering for Scalar Propagators in (Anti and) de Sitter Spacetimes

TL;DR

This thesis reviews and applies a configuration space method to compute scalar propagators in AdS and dS spacetimes, avoiding mode summation and analytic continuation, and provides insights into their geometric and conformal properties.

Contribution

It extends a configuration space method to arbitrary dimensions for AdS and dS spacetimes, offering a direct computation of propagators with conformal dimensions without mode summation.

Findings

Method successfully computes propagators in AdS and dS without mode summation.

Results agree with existing literature on propagators and conformal dimensions.

Provides a comprehensive overview of geometric properties of AdS and dS 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 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.