2PI functional techniques for gauge theories: QED

Abstract

We discuss the formulation of the prototype gauge field theory, QED, in the context of two-particle-irreducible (2PI) functional techniques with particular emphasis on the issues of renormalization and gauge symmetry. We show how to renormalize all $n$-point vertex functions of the (gauge-fixed) theory at any approximation order in the 2PI loop-expansion by properly adjusting a finite set of local counterterms consistent with the underlying gauge symmetry. The paper is divided in three parts: a self-contained presentation of the main results and their possible implementation for practical applications; a detailed analysis of ultraviolet divergences and their removal; a number of appendices collecting technical details.

65 pages, 18 figures

References in corpus (10)

• Quantum field thermalization in expanding backgrounds
• Comparison of Boltzmann Kinetics with Quantum Dynamics for a Chiral Yukawa Model Far From Equilibrium
• QED Electrical Conductivity using the 2PI Effective Action
• Renormalized Finite Temperature phi^4 theory from the 2PI Effective Action
• Ward Identities for the 2PI effective action in QED
• The pressure of QED from the two-loop 2PI effective action
• Thermal effects on slow-roll dynamics
• Counterterm resummation for 2PI-approximation in constant background
• Particle creation and warm inflation
• Renormalization of 2PI resummation: a renormalization scheme approach

Cited by in corpus (24)

• Confinement from Correlation Functions
• 2PI effective action for the SYK model and tensor field theories
• Renormalization group methods and the 2PI effective action
• Non-renormalizability of the classical statistical approximation
• The 2PI effective theory at next-to-leading order using the functional renormalization group
• Functional renormalization group and 2PI effective action formalism
• The 2PI effective action at four loop order in ${\phi }^4$ theory
• Collisional strong-field QED kinetic equations from first principles
• Renormalization group flow equations connected to the $n$PI effective action
• Broken phase scalar effective potential and Phi-derivable approximations
• Towards thermalization in heavy-ion collisions: CGC meets the 2PI formalism
• Bethe-Salpeter Equations from the 4PI effective action
• 4-point vertices from the 2PI and 4PI Effective Actions
• Resummations in the Bloch-Nordsieck model
• A new method to calculate the n-Particle Irreducible Effective Action
• A critical look at the role of the bare parameters in the renormalization of Phi-derivable approximations
• Renormalization of the 4PI effective action using the functional renormalization group
• Validating the 2PI resummation: the Bloch-Nordsieck example
• Broken symmetry phase solution of the phi^4 model at two-loop level of the Phi-derivable approximation
• Renormalization out of equilibrium in a superrenormalizable theory
• Zero point energy of composite particles: The medium effects
• Computing Early-time Dynamics in Heavy Ion Collisions: Status, Problems and Prospects
• 2PI Effective Action and Evolution Equations of N = 4 super Yang-Mills
• A new resummation scheme in scalar field theories