  The covariant Hamiltonian formulation for general relativity is studied in
terms of self-dual variables on a manifold with an internal and lightlike
boundary. At this inner boundary, new canonical variables appear: a spinor and
a spinor-valued two-form that encode the entire intrinsic geometry of the null
surface. At a two-dimensional cross-section of the boundary, quasi-local
expressions for the generators of two-dimensional diffeomorphisms, time
translations, and dilatations of the null normal are introduced and written in
terms of the new boundary variables. In addition, a generalisation of the
first-law of black-hole thermodynamics for arbitrary null surfaces is found,
and the relevance of the framework for non-perturbative quantum gravity is
stressed and explained.
