# Ward Identities for the 2PI effective action in QED

1 APC - THEORIE
APC (UMR_7164) - AstroParticule et Cosmologie, Institut für theoretische Physik
Abstract : We study the issue of symmetries and associated Ward-like identities in the context of two-particle-irreducible (2PI) functional techniques for abelian gauge theories. In the 2PI framework, the n-point proper vertices of the theory can be obtained in various different ways which, although equivalent in the exact theory, differ in general at finite approximation order. We derive generalized (2PI) Ward identities for these various n-point functions and show that such identities are exactly satisfied at any approximation order in 2PI QED. In particular, we show that 2PI-resummed vertex functions, i.e. field-derivatives of the so-called 2PI-resummed effective action, exactly satisfy standard Ward identities. We identify another set of n-point functions in the 2PI framework which exactly satisfy the standard Ward identities at any approximation order. These are obtained as field-derivatives of the two-point function $\bar G^{-1}[\phi]$, which defines the extremum of the 2PI effective action. We point out that the latter is not constrained by the underlying symmetry. As a consequence, the well-known fact that the corresponding gauge-field polarization tensor is not transverse in momentum space for generic approximations does not constitute a violation of (2PI) Ward identities.
Document type :
Journal articles

http://hal.in2p3.fr/in2p3-00180991
Contributor : Simone Lantz <>
Submitted on : Monday, October 22, 2007 - 4:44:32 PM
Last modification on : Wednesday, October 21, 2020 - 4:32:14 PM

### Citation

U. Reinosa, J. Serreau. Ward Identities for the 2PI effective action in QED. Journal of High Energy Physics, Springer, 2007, 11, pp.097. ⟨10.1088/1126-6708/2007/11/097⟩. ⟨in2p3-00180991⟩

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