Implications of analyticity to solution of Schwinger-Dyson equations in Minkowski space

Abstract

We review some recent developments in nonperturbative studies of quantum field theory (QFT) using the Schwinger-Dyson equations formulated directly in Minkowski space. We begin with the introduction of essential ideas of the integral representation in QFT and a discussion of renormalization in this approach. The technique based on the integral representation of Green's functions is exploited to solve Schwinger-Dyson equations in several quantum field models, eg. in scalar models and in strong coupling $QE{D}_{3+1}$ in the quenched and in the unquenched approximation. The phenomenon of dynamical chiral symmetry breaking in regularized theory is touched. In QCD, the analyticity of gluon propagator on the complex momentum square plane is exploited to continue some recent lattice data to timelike momentum axis. We find non-positive absorptive part contribution in the Landau gauge gluon propagator which is in agreement with some other new recent analyzes.

57 pages, Sections slightly reorganized, one section devoted to CHSB added, references changed, accepted in Few-body Systems

References in corpus (4)

• A dynamical gluon mass solution in a coupled system of the Schwinger-Dyson equations
• Analytic Invariant Charge in QCD
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• The Gluon Propagator in Minkowski and Euclidean Space: Role of an A^2 Condensate

Cited by in corpus (13)

• Quantitative studies of the homogeneous Bethe-Salpeter Equation in Minkowski space
• Schwinger functions and light-quark bound states
• Solving the Bethe-Salpeter equation for a pseudoscalar meson in Minkowski space
• Quark propagator in Minkowski space
• Dynamical chiral symmetry breaking with Minkowski space integral representations
• Dynamical mass generation in Minkowski space at QCD scale
• Padé approximants and analytic continuation of Euclidean Phi-derivable approximations
• Confined gluon from Minkowski space continuation of PT-BFM SDE solution
• The quark spectral functions and the Hadron Vacuum Polarization from application of DSEs in Minkowski space
• Gauge Technique approximation to the $\pi \gamma$ production and the pion transition form factor
• Extracting a model quark propagator's spectral density
• Quark Schwinger-Dyson equation in temporal Euclidean space
• Minkowski-space solutions of the Schwinger-Dyson equation for the fermion propagator with the rainbow-ladder truncation