  To set up a self-consistent quantum field theory of degenerate systems, the
unperturbed state should be described by a density matrix instead of a pure
state. This increases the combinatorial complexity of the many-body equations.
Hopf algebraic techniques are used to deal with this complexity and show that
the Schwinger-Dyson equations are modified in a non-trivial way. The hierarchy
of Green functions is derived for degenerate systems, and the case of a single
electron in a two-fold degenerate orbital is calculated in detail.
