Seminarium Teorii Względności i Grawitacji

The physics of gauge theories in the presence of spacetime boundaries has been known to produce very interesting results and concrete phenomena from the discovery of the Quantum Hall effect to the modern developments in holography and, more recently, the "Corner proposal" which suggest an approach to the problem of Quantum Gravity through the use of symmetries. In this talk, we will review the classical covariant formulation of Yang-Mills theory and general relativity in the presence of spacetime boundaries. In order to do so we start by giving a short introduction the the covariant phase space formalism, focusing mainly on the derivation of the presymplectic forms and their properties. We further revisit the introduction of the edge modes and the conditions which justify them, in the context where only field-independent gauge transformations are considered. In particular, we show that the presence of edge modes is not justified by gauge invariance of the presymplectic form, but rather by the condition that the presymplectic form is degenerate on the initial field space, which allows to relate this presymplectic form to the symplectic form on the gauge reduced field space via pullback.