Observable symmetries as a type of holism

The natural interpretation of asymptotic conditions on Yang-Mills theory and general relativity is as defining types of isolated subsystems.

We can think of asymptotic symmetries as providing different relations between observer and subsystem, and thus as providing physically distinct possibilities composed of the same (idealized) parts. We would like to apply this asymptotic notion to finite regions. But the non-locality of Yang-Mills and GR are an obstacle to the description of physical degrees of freedom intrinsic to subsystems occupying finite regions.

Here I will extract those YM gauge-invariant degrees of freedom that are independent of external conditions (which we label horizontal). It turns out that these degrees of freedom alone are enough for composing subsystems. This allows us to relate bulk conserved charges to those subsystem rigid symmetries that are holistically ‘observable’.