Identical Relations among Transverse Parts of Variant Green Functions and the Full Vertices in Gauge Theories

Abstract

The identical relations among the transverse parts of variant vertex functions are derived by computing the curl of the time-ordered products of three-point Green functions involving the vector, the axial-vector and the tensor current operators, respectively. These transverse relations are coupled each other. Combining these transverse relations with the normal (longitudinal) Ward-Takahashi identities forms a complete set of constraint relations for three-point vertex functions. As a consequence, the full vector, the full axial-vector and the full tensor vertex functions in the momentum space are exactly obtained.

12 pages, revtex

Cited by in corpus (10)

• Ward-Green-Takahashi identities and the axial-vector vertex
• Progress in vacuum susceptibilities and their applications to the chiral phase transition of QCD
• Checking the transverse Ward-Takahashi relation at one loop order in 4-dimensions
• Transverse Symmetry Transformations and the Quark-Gluon Vertex Function in QCD
• Transverse Ward-Takahashi Relation for the Fermion-Boson Vertex Function in 4-dimensional QED
• How gauge covariance of the fermion and boson propagators in QED constrain the effective fermion-boson vertex
• Quantum anomaly of the transverse Ward-Takahashi relation for the axial-vector vertex
• Calculation of tensor susceptibility beyond rainbow-ladder approximation of Dyson-Schwinger equations approach
• Gauge Technique approximation to the $\pi \gamma$ production and the pion transition form factor
• Transverse Ward-Takahashi Identities and Full Vertices Functions in Different Representation in QED${}_3$