  I consider the problem of defining canonical coordinates and momenta in pure
Yang-Mills theory, under the condition that Gauss' law is identically
satisifed. This involves among other things particular boundary conditions for
certain dependent variables. These boundary conditions are not postulated a
priori, but arise as consistency conditions related to the equations of motion.
It is shown that the theory indeed has a canonical structure, provided one uses
a special gauge condition, which is a natural generalisation to Yang-Mills
theory of the Coulomb gauge condition in electrodynamics. The canonical
variables and Hamiltonian are explicitly constructed. Quantisation of the
theory is briefly discussed.
