Variational Quantum Electrodynamics

Abstract

A variational method is discussed, based on the principle of minimal variance. The method seems to be suited for gauge interacting fermions, and the simple case of quantum electrodynamics is discussed in detail. The issue of renormalization is addressed, and the renormalized propagators are shown to be the solution of a set of finite integral equations. The method is proven to be viable and, by a spectral representation, the multi-dimensional integral equations are recast in one-dimensional equations for the spectral weights. The UV divergences are subtracted exactly, yielding a set of coupled Volterra integral equations that can be solved iteratively, and are known to have a unique solution.

In Section II the method of arXiv:1308.1836 is reviewed and used for QED

References in corpus (6)

• Higher order extensions of the Gaussian effective potential
• Gaussian Effective Potential and superconductivity
• Self-consistent variational approach to the minimal left-right symmetric model of electroweak interactions
• A general interpolation scheme for thermal fluctuations in superconductors
• Gaussian effective potential for the standard model SU(2)xU(1) electroweak theory
• Incorporating fermions in the Gaussian Effective Potential: the Higgs-Top Sector

Cited by in corpus (12)

• Analytical study of Yang-Mills theory in the infrared from first principles
• Analytic structure of QCD propagators in Minkowski space
• The gluon propagator in Feynman gauge by the method of stationary variance
• Second order gluon polarization for SU(N) theory in linear covariant gauge
• Variational study of mass generation and deconfinement in Yang-Mills theory
• Dispersion relations for unphysical particles
• The Principle of Stationary Variance in Quantum Field Theory
• Universal scaling of gluon and ghost propagators in the infrared
• The Nielsen identities in screened theories
• Analytic continuation and physical content of the gluon propagator
• Screened massive expansion of Schwinger-Dyson equations
• Screened massive expansion of the quark propagator in the Landau gauge