These notes are a transcript of lectures given by the author in the XVIII Modave summer
school in mathematical physics. The introduction is devoted to a detailed review of the …

We develop a framework based on the covariant phase space formalism that identifies
gravitational edge modes as dynamical reference frames. As such, they enable both the …

The following questions are germane to our understanding of gauge-(in) variant quantities
and physical possibility: in which ways are gauge transformations and spacetime …

It is recalled how relationality arises as the core insight of general‐relativistic gauge field
theories from the articulation of the generalized hole and point‐coincidence arguments …

We make a case for the unique relevance of Cartan geometry for gauge theories of gravity
and supergravity. We introduce our discussion by recapitulating historical threads, providing …

Abstract Soft symmetries for Yang–Mills theory are shown to correspond to the residual
Hamiltonian action of the gauge group on the Ashtekar–Streubel phase space, which is the …

Gauge symmetries play a central role, both in the mathematical foundations as well as the
conceptual construction of modern (particle) physics theories. However, it is yet unclear …

The dressing field method for diffeomorphisms: a relational framework - IOPscience Skip to
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We study gauge theories on spacetime manifolds with a codimension-$1 $ submanifold with
boundary. We characterise the reduced phase space of the theory whenever it is described …

A bstract The group of vertical diffeomorphisms of a principal bundle forms the action Lie
groupoid associated to the bundle. The former is generated by the group of maps with value …