Resummations in the Bloch-Nordsieck model

Abstract

We studied different levels of resummations of the exactly solvable Bloch-Nordsieck model in order to be able to compare the approximations with an exact result. We studied one-loop perturbation theory, 2PI resummation and Schwinger-Dyson equations truncated in a way to maintain Ward-identities. At all levels we carefully performed renormalization. We found that although the 2PI resummation does not exhibit infrared sensitivity at the mass shell (the one-loop perturbation theory does), but it is still far from the exact solution. The method of truncated Schwinger-Dyson equations, however, is exact in this model, so it provides a new way of solving the Bloch-Nordsieck model. This method can also be generalized to other, more complicated theories.

12 pages, 3 figures, revtex4

References in corpus (5)

• QED Electrical Conductivity using the 2PI Effective Action
• The pressure of QED from the two-loop 2PI effective action
• Counterterm resummation for 2PI-approximation in constant background
• Renormalization of O(N) model in 1/N expansion in auxiliary field formalism
• Renormalization of 2PI resummation: a renormalization scheme approach

Cited by in corpus (12)

• The 2PI effective theory at next-to-leading order using the functional renormalization group
• The 2PI effective action at four loop order in ${\phi }^4$ theory
• Exact Solutions to the Fermion Propagator Schwinger-Dyson Equation in Minkowski space with on-shell Renormalization for Quenched QED
• Non-perturbative emergence of non-Fermi liquid behaviour in $d=2$ quantum critical metals
• Attempts at a determination of the fine-structure constant from first principles: A brief historical overview
• Theory of Phonon-Assisted Adsorption in Graphene: Many-Body Infrared Dynamics
• Spectral function of the Bloch-Nordsieck model at finite temperature
• Validating the 2PI resummation: the Bloch-Nordsieck example
• Quasiparticles in an interacting system of charge and monochromatic field
• Shear viscosity over entropy density ratio with extended quasi-particles
• Statistical theory of photon gas in plasma
• Infrared multiphoton resummation in quantum electrodynamics