Constructing the theory at the boundary, its dynamics and degrees of freedom

Understand

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.