  Given a theory in a region of space-time with boundaries, defined by a
Lagrangian, we propose a method to find the corresponding theory at the
boundary (either space-like or time-like), that allows us to identify the
degrees of freedom at the boundary without any gauge fixing nor further
assumptions a priori. We start by finding the corresponding action principle at
the boundary. From this, we can find the corresponding equations of motion, the
symmetries and degrees of freedom at the boundary. Then we characterise the
degrees of freedom at the boundary. We exemplify this method by analysing the
broadly studied 3-dimensional Abelian Chern-Simons theory. We found, through
the Hamiltonian framework, that the boundary theory has one degree of freedom
that can be characterised by the chiral boson: the Quantum Hall edge modes. We
also find a correspondence between a gauge fixing in the bulk with a boundary
condition and discuss whether this is enough to have a well-posed action
principle and the possible scenarios.
