Ward-Takahashi identities for a scalar field on de Sitter space with gauged Weyl symmetry

Abstract

This thesis explores a recently developed approach to rescaling symmetry of quantum field theories in an extension of general relativity. Unfortunately it has not been named yet, but the model developed by Lucat and Prokopec is best described as gauging Weyl transformations by a vector field interpreted as space-time torsion. After introducing Riemann-Cartan geometry as extension of general gelativity with torsion, the appropriate gauge connection is constructed. A massless, non-minimally coupled scalar field on de Sitter space is selected to test for the conformal anomaly in the framework of the new theory. Integrating out the scalar fluctuations yields an effective field theory description, that is determined to one loop in the scalar field and up to second order in external graviton and torsion perturbations. By renormalizing the corresponding vertex functions using dimensional regularization, the Ward-Takahashi identities are shown to remain consistent to arbitrary linear perturbations. The results are discussed in the context of the trace anomaly.