Quantum Yang-Mills field theory

@article{Frasca2017QuantumYF,
  title={Quantum Yang-Mills field theory},
  author={Marco Frasca},
  journal={The European Physical Journal Plus},
  year={2017},
  volume={132},
  pages={1-11}
}
  • M. Frasca
  • Published 17 September 2015
  • Mathematics
  • The European Physical Journal Plus
Abstract.We show that the Dyson-Schwinger set of equations for the Yang-Mills theory can be exactly solved till the two-point function. This is obtained given a set of nonlinear waves solving the classical equations of motion. Translation invariance is maintained by the proper choice of the solution of the equation for the two-point function as devised by Coleman. The computation of the Dyson-Schwinger equations is performed in the same way as devised by Bender, Milton and Savage providing a… 
Differential Dyson–Schwinger equations for quantum chromodynamics
Using a technique devised by Bender, Milton and Savage, we derive the Dyson–Schwinger equations for quantum chromodynamics in differential form. We stop our analysis to the two-point functions. The
Confinement in a three-dimensional Yang–Mills theory
We show that, starting from known exact classical solutions of the Yang–Mills theory in three dimensions, the string tension is obtained and the potential is consistent with a marginally confining
Confinement and renormalization group equations in string-inspired nonlocal gauge theories
As an extension of the weak perturbation theory obtained in recent analysis on infinite-derivative non-local non-Abelian gauge theories motivated from p-adic string field theory, and postulated as
Confinement studies in QCD with Dyson-Schwinger equations
  • M. Frasca
  • Physics
    Nuclear and Particle Physics Proceedings
  • 2021
Some remarks on the spectral functions of the Abelian Higgs model
We consider the unitary Abelian Higgs model and investigate its spectral functions at one-loop order. This analysis allows to disentangle what is physical and what is not at the level of the
The BRST-invariant vacuum state of the Gribov–Zwanziger theory
We revisit the effective action of the Gribov-Zwanziger theory, taking into due account the BRST symmetry and renormalization (group invariance) of the construction. We compute at one loop the
Nonlocal Nambu–Jona-Lasinio model and chiral chemical potential
  • M. Frasca
  • Physics
    The European Physical Journal C
  • 2018
We derive the critical temperature in a nonlocal Nambu–Jona-Lasinio model with the presence of a chiral chemical potential. The model we consider uses a form factor derived from recent studies of the
Confinement in QCD and generic Yang-Mills theories with matter representations
We derive the low-energy limit of quantum chromodynamics (QCD) and show that in the ’t Hooft limit, i.e. for a very large number of colors and increasing ’t Hooft coupling, quark confinement is
...
...

References

SHOWING 1-10 OF 32 REFERENCES
Solution of Schwinger-Dyson equations for PT symmetric quantum field theory
In recent papers it has been observed that non-Hermitian Hamiltonians, such as those describing ig� 3 and −g� 4 field theories, still possess real positive spectra so long as the weaker condition of
Exact solutions for classical Yang-Mills fields
We provide a set of exact solutions of the classical Yang-Mills equations. They have the property to satisfy a massive dispersion relation and hold in all gauges. These solutions can be used to
Nonunique solution to the Schwinger-Dyson equations.
TLDR
It is shown that while the Schwinger-Dyson equations do determine the weak-coupling perturbation expansions of the Green's functions, the solution to the SchwINGER- Dyson equations is not unique and therefore the nonperturbative content of theGreen's functions remains undetermined.
Lorentz Covariant Quantization of Nonlinear Waves
The quantum theory of a real scalar field in one space dimension with quartic coupling is studied as an example of a field theory possessing exact classical solutions representing extended
Mapping a Massless Scalar Field Theory on a Yang-Mills Theory: Classical Case
We analyze a recent proposal to map a massless scalar field theory onto a Yang-Mills theory at classical level. It is seen that this mapping exists at a perturbative level when the expansion is a
Canonical quantization of nonlinear waves
By means of a canonical transformation we investigate nonlinear field theories that possess exact classical solutions. This transformation is equivalent to the method of collective coordinates
The S Matrix in Quantum Electrodynamics
The covariant quantum electrodynamics of Tomonaga, Schwinger, and Feynman is used as the basis for a general treatment of scattering problems involving electrons, positrons, and photons. Scattering
A Solution to Coupled Dyson-Schwinger Equations for Gluons and Ghosts in Landau Gauge
A truncation scheme for the Dyson{endash}Schwinger equations of QCD in Landau gauge is presented which implements the Slavnov{endash}Taylor identities for the 3-point vertex functions. Neglecting
Nonperturbative confinement in quantum chromodynamics: I. Study of an approximate equation of Mandelstam
An approximated form of the Dyson–Schwinger equation for the gluon propagator in quarkless QCD is subjected to nonlinear functional and numerical analysis. It is found that solutions exist, and that
...
...