The Nielsen Identities for the generalized $R_ξ$-gauge

We show that it is possible, in opposition to a previous conjecture, to derive a Nielsen identity for the effective action in the case of the generalized $R_ξ$-gauge, where the gauge function explicitly depends on the gauge parameter $ξ$. Also the Nielsen identity for the effective potential is verified to one-loop in the Abelian Higgs model and the corresponding identity for the physical Higgs mass is derived.

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