Transverse Ward-Takahashi Relation for the Vector Vertex in Quantum Field Theory

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The transverse Ward-Takahashi (W-T) relation for the vector vertex in quantum field theory is derived by calculating the curl of the time-ordered product of the three-point function including the vector current operator. This provides the constraint on the transverse part of the vertex. By combining the transverse and normal (longitudinal)W-T identities, we obtain the expression for the full vector vertex function.``
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