Quantization of gauge fields, graph polynomials and graph cohomology

Understand

We review quantization of gauge fields using algebraic properties of 3-regular graphs.

• We derive the Feynman integrand at n loops for a non-abelian gauge theory quantized in a covariant gauge from scalar integrands for connected 3-regular graphs, obtained from the two Symanzik polynomials.
• The transition to the full gauge theory amplitude is obtained by the use of a third, new, graph polynomial, the corolla polynomial.
• This implies effectively a covariant quantization without ghosts, where all the relevant signs of the ghost sector are incorporated in a double complex furnished by the corolla polynomial -we call it cycle homology- and by graph homology.