The QCD Ward Identity in Axial Gauge is a fundamental symmetry in quantum chromodynamics (QCD), the theory of strong interactions. It relates the behavior of the theory under a gauge transformation to the behavior under a chiral transformation.
The QCD Ward Identity is important because it is a key tool for understanding the behavior of QCD at high energies. It is also crucial for making predictions and calculations in experiments involving strong interactions, such as those at the Large Hadron Collider.
The QCD Ward Identity is closely related to chiral symmetry breaking, which is a phenomenon in which the symmetry between left- and right-handed particles is broken. The identity allows us to study the effects of chiral symmetry breaking and how it affects the behavior of QCD.
The QCD Ward Identity is related to the Goldstone theorem, which states that when a continuous symmetry is spontaneously broken, there must be a massless particle associated with the broken symmetry. In QCD, this particle is the pion, and the QCD Ward Identity helps us understand its role in the theory.
The QCD Ward Identity is used in practical calculations by allowing us to simplify and constrain the calculation of certain quantities in QCD. It can be used to derive relations between different observables that are experimentally measured, making it a powerful tool for testing the theory and making predictions.