Gauges, propagators, and physics

When a theory shall be described at all scales, it is necessary to start from its elementary degrees of freedom. Herein, one possible chain of steps for this purpose will be briefly outlined for the example of a gauge theory, like QCD. Starting with the elementary constituents, gluons and quarks, step by step the final observables, physical states, will be built up. This process is based on the elementary correlation functions, and uses a combination of both numerical lattice calculations and functional continuum methods. While the process uses a fixed gauge at each intermediate step, the final observables are gauge-invariant.