Speaker
Andrea Quadri
(INFN, Sez. di Milano)
Description
It sometimes happens that particular gauges are computationally more suited than others in the study of several properties of gauge theories.
QCD provides a number of examples of such a feature: for instance,
evolution equations in the Color Glass Condensate picture are usually derived in the Light-Cone gauge. A more striking example is given by massive solutions
of appropriate truncations to the QCD Schwinger-Dyson equations, that
have been shown to exist in the Landau gauge, confirming lattice simulations
carried out in the same gauge.
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 $\alpha$ in Yang-Mills theories is controlled by a canonical flow that explicitly solves the Nielsen identities of the model.
Green's functions in the $\alpha$ 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
$\alpha$-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.
Author
Andrea Quadri
(INFN, Sez. di Milano)