Abstract
In quantum field theories with massless gauge bosons, the conventional formulation of scattering amplitudes in terms of momentum eigenstates lead to infrared divergences. To resolve this one should dress charged particles with an infinite number of low-energy (soft) gauge bosons. These dressings are closely related to the asymptotic symmetries of the the- ory. The aim of this dissertation is to investigate this relation in detail, and study the implications of dressings in a quantum field theoretical context in asymptotically flat and Schwarzschild spacetimes. In particular, the asymptotic symmetry of interest in gravity is the BMS supertranslation. First, we demonstrate in perturbative quantum gravity that the dressings facilitate charge conservation by carrying a definite supertranslation charge. We then use this property to derive dressed states from the charge conservation laws of asymp- totic symmetries. We develop a unified quantum mechanical framework for the construction of dressings at the null infinity and the horizon of a Schwarzschild black hole, and show that the black hole soft hairs are planted on the horizon by dressed particles falling into the black hole. This framework is then extended to the magnetic parity soft charges of electro- magnetism and gravity. It is shown that one can construct ’t Hooft line dressings at the asymptotic boundaries, which are charged under the magnetic large gauge transformations and the dual supertranslations. Finally, we study the standard and dual supertranslation charges at the black hole horizon. We find central terms in their algebra in the presence of singularities in the parameter functions, which hints at further interesting soft structures yet to be revealed.
Published Version
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