The most commonly used metod of derivation of quantities in quantum field theory uses Feynman diagrams and Feynman propagators. Unfortunately, when applied to gauge theories, it mostly ignores the gauge symmetry, which becomes obscured at intermediate steps, and even in the final result it's not always visible. However, there exists a manifestly covariant way to make calculations within a quantum field theory, with the use of gauge field-dependent propagators instead of the free-field Feynman propagators.

I'm going to present a way to derive gauge field-dependent propagators in the form that can be used in perturbative calculations made with Feynman diagrams and to show how this form can make the derivation of the chiral anomaly quick and transparent, as well as the way it shows how certain regularizations break Ward identites.