Transverse symmetry transformations and the quark-gluon vertex function in QCD

The transverse symmetry transformations associated with the normal symmetry transformations in gauge theories are introduced, which at first are used to reproduce the transverse Ward-Takahashi identities in the Abelian theory QED. Then the transverse symmetry transformations associated with the BRST symmetry and chiral transformations in the non-Abelian theory QCD are used to derive the transverse Slavnov-Taylor identities for the vector and axial-vector quark-gluon vertices, respectively. Based on the set of normal and transverse Slavnov-Taylor identities, an expression of the quark-gluon vertex function is derived, which describes the constraints on the structure of the quark-gluon vertex imposed from the underlying gauge symmetry of QCD alone. Its role in the study of the Dyson-Schwinger equation for the quark propagator in QCD is discussed.