Ward-Takahashi identities from symmetry

nlieb
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Does anyone know how to derive the Ward-Takahashi identity for a field starting from a known conserved Noether current (or equally helpful, from a known symmetry transformation of the Lagrangian)? It'll probably be enough to allow me to do it for myself if you could explain quantitatively what the Ward-Takahashi identity is. Please don't quote wikipedia to me, from a pedagogical standpoint it has all the teaching prowess of an amoeba.
 
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Srednicki's http://web.physics.ucsb.edu/~mark/ms-qft-DRAFT.pdf" , equation 67.8 onwards has some relevant discussion.
 
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Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. Towards the end of the first lecture for the Qiskit Global Summer School 2025, Foundations of Quantum Mechanics, Olivia Lanes (Global Lead, Content and Education IBM) stated... Source: https://www.physicsforums.com/insights/quantum-entanglement-is-a-kinematic-fact-not-a-dynamical-effect/ by @RUTA
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