Connecting amplitudes in different gauges beyond perturbation theory: a canonical flow approach

Physical quantities in gauge theories have to be gauge-independent. However their evaluation can be greatly simplified by working in particular gauges. Since physical quantities have to be gauge invariant, it is important to establish an approach allowing the comparison of computations carried out in different gauges even beyond perturbation theory. We show that the dependence on the gauge parameter $\alpha =0$ in Yang-Mills theories is controlled by a canonical flow that explicitly solves the Nielsen identities of the model. Green’s functions in the $\alpha =0$ gauge are given by amplitudes evaluated in the theory at $\alpha =0$ (e.g., in the example of Lorentz-covariant gauges, in terms of Landau gauge amplitudes) plus some contributions induced by the $\alpha =0$-dependence of the generating functional of the canonical flow. Explicit formulas are presented and an application of the formalism to the gluon propagator is discussed.