Ward Identities for the 2PI effective action in QED

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 $\bcG^{-1}[ϕ]$, 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. More generally, our analysis demonstrates that approximation schemes based on 2PI functional techniques respect all the Ward identities associated with the underlying abelian gauge symmetry. Our results apply to arbitrary linearly realized global symmetries as well.

33 pages, 2 figures

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• Collisional strong-field QED kinetic equations from first principles
• Non-equilibrium Quantum Spin Dynamics from 2PI Functional Integral Techniques in the Schwinger Boson Representation
• Towards thermalization in heavy-ion collisions: CGC meets the 2PI formalism
• The pressure of QED from the two-loop 2PI effective action
• Effective convergence of the 2PI-1/N expansion for nonequilibrium quantum fields
• Counterterm resummation for 2PI-approximation in constant background
• Study of chiral symmetry restoration in linear and nonlinear O(N) models using the auxiliary field method
• A new method to calculate the n-Particle Irreducible Effective Action
• Two-particle irreducible effective action approach to nonlinear current conserving approximations in driven systems
• 2PI functional techniques for abelian gauge theories