Quantum field theory of degenerate systems

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.