Hamiltonian study of the asymptotic symmetries of gauge theories

Abstract

Asymptotic symmetries are a general and important feature of theories with long-ranging fields, such as gravity, electromagnetism, and Yang-Mills. They appear in the formalism once the analytic behaviour of fields near infinity is specified and have received a renewed interest in the last years after a possible connection with the information-loss paradox has been conjectured.

One of the various methods used to study the asymptotic symmetries of field theories relies on the Hamiltonian formalism and was introduced in the seminal work of Henneaux and Troessaert, who successfully applied it to the case of gravity and electrodynamics, thereby deriving the respective asymptotic symmetry groups of these theories. The main advantage of this approach is that the study of the asymptotic symmetries ensues from clear-cut first principles. These include the minimal assumptions that are necessary to ensure the existence of Hamiltonian structures (phase space, symplectic form, differentiable Hamiltonian) and, in case of Poincaré invariant theories, a canonical action of the Poincaré group.

In this thesis, after an extensive review of how the Hamiltonian approach to study asymptotic symmetries of gauge theories works, we apply these methods to two specific situations of physical interest. First, we deal with the non-abelian Yang-Mills case and we show that the above principles lead to trivial asymptotic symmetries (nothing else than the Poincaré group) and, as a consequence, to a vanishing total colour charge. This is a new and somewhat unexpected result. It implies that no globally colour-charged states exist in classical non-abelian Yang-Mills theory.

The second situation considered in this thesis is a scalar field minimally-coupled to an abelian gauge field, which can be used to study, at the same time, two specific cases: scalar electrodynamics and the abelian Higgs model. We show that the situation in scalar electrodynamics amply depends on whether the scalar field is massive or massless, insofar as, in the latter case, one cannot canonically implement asymptotic symmetries. Furthermore, we illustrate that, in the abelian Higgs model, the asymptotic canonical symmetries reduce to the Poincaré group in an unproblematic fashion.