Infrared problem in the Faddeev–Popov sector in Yang–Mills Theory and Perturbative Gravity

In a broad class of spacetimes including de Sitter space, the Faddeev–Popov ghost propagator is infrared-divergent in both BRST-quantised Yang–Mills theory and BRST-quantised perturbative gravity. Introducing a mass term for infrared regularisation, one may delete an infrared-divergent term from the propagator before taking the massless limit. This obtains an effective zero-mode sector Feynman propagator that is infrared-convergent and exhibits appropriate spacetime symmetries, such as de Sitter invariance in de Sitter space and time translation invariance on a flat static torus. This prescription, which dates to 2008, relies on free integration by parts (a term explained on page 11), so its generality to a broad class of spacetimes is limited. A further difficulty is that this prescription introduces a mass term in the action that breaks the theory’s Becchi–Rouet–Stora–Tyutin invariance and anti-Becchi–Rouet–Stora–Tyutin invariance. This thesis presents an alternative prescription in which it is shown that the modes responsible for the Faddeev–Popov ghost propagator’s infrared divergence are cyclic in the Lagrangian formalism. These modes can then be obviated from the Lagrangian, Hamiltonian and Schrödinger wave functional formalisms. Neither of the aforementioned difficulties with the old prescription apply to the newer one discussed herein, which manifestly preserves both internal symmetries throughout. The prescriptions have equivalent perturbation theories in spacetimes in which free integration by parts is possible. The new prescription can then be regarded as a generalisation of the 2008 prescription to a broader class of spacetimes.