In field theory, when 4-divergences of time-ordered Green's functions are computed, there are extra terms known as 'Schwinger terms'.

When deriving the quantum equations of motion for time-ordered Green's functions, there are extra terms known as 'Contact terms'.

Are contact terms and Schwinger terms one and the same? Or is one a special case of the other? Or are they completely unrelated things? [There's also some kind of relationship with $\mathcal{L}_\text{int}\neq\mathcal{H}_\text{int}$, when I can't place my finger on.]

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    $\begingroup$ Suggestion to the question (v1): While you are at it, you could also ask about 'Seagull terms'. $\endgroup$ – Qmechanic Apr 6 '13 at 23:16

They are different.

'Schwinger terms' arise as central or abelian (or even non-abelian) extensions of current algebras of operators, very often as a consequence of the regularization procedure. They are source of anomalies. The original paper is short and readable: Field theory and commutators by J. Schwinger. You can read more in Moshe's answer to my question Classical and quantum anomalies and references therein.

On the other hand, 'contact terms' are terms that show up when different fields are evaluated at the same point. They are present in the Schwinger-Dyson equations and in Ward identities, for example. See Schwinger-Dyson equation on Wikipedia and Maimon's answer (or mine) to this question On-shell symmetry from a path integral point of view.


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