  In [1, 2, 3] the Corolla Polynomial $ \mathcal C (\Gamma) \in \mathbb C
[a_{h_1}, \ldots, a_{h_{\left \vert \Gamma^{[1/2]} \right \vert}}] $ was
introduced as a graph polynomial in half-edge variables $ \left \{ a_h \right
\} _{h \in \Gamma^{[1/2]}} $ over a 3-regular scalar quantum field theory (QFT)
Feynman graph $ \Gamma $. It allows for a covariant quantization of pure
Yang-Mills theory without the need for introducing ghost fields, clarifies the
relation between quantum gauge theory and scalar QFT with cubic interaction and
translates back the problem of renormalizing quantum gauge theory to the
problem of renormalizing scalar QFT with cubic interaction (which is super
renormalizable in 4 dimensions of spacetime). Furthermore, it is, as we
believe, useful for computer calculations. In [4] on which this paper is based
the formulation of [1, 2, 3] gets slightly altered in a fashion specialized in
the case of the Feynman gauge. It is then formulated as a graph polynomial $
\mathcal C ( \Gamma ) \in \mathbb C [a_{h_{1 \pm}}, \ldots, a_{h_{\left \vert
\Gamma^{[1/2]} \right \vert} \vphantom{h}_\pm}, b_{h_1}, \ldots, b_{h_{\left
\vert \Gamma^{[1/2]} \right \vert}}] $ in three different types of half-edge
variables $ \left \{ a_{h_+} , a_{h_-} , b_h \right \} _{h \in \Gamma^{[1/2]}}
$. This formulation is also suitable for the generalization to the case of
spontaneously broken gauge theories (in particular all bosons from the Standard
Model), as was first worked out in [4] and gets reviewed here.
