311 research outputs found
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 't~Hooft limit of color
number going to infinity is derived showing how these equations can be cast
into a treatable even if approximate form. It is seen how this limit gives a
sound description of the low-energy behavior of quantum chromodynamics by
discussing the dynamical breaking of chiral symmetry and confinement, providing
a condition for the latter. This approach exploits a background field technique
in quantum field theory.Comment: 20 pages, 2 figures. Version accepted for publication in European
Physical Journal
Infrared Gluon and Ghost Propagators
We derive the form of the infrared gluon propagator by proving a mapping in
the infrared of the quantum Yang-Mills and theories. The
equivalence is complete at a classical level. But while at a quantum level, the
correspondence is spoiled by quantum fluctuations in the ultraviolet limit, we
prove that it holds in the infrared where the coupling constant happens to be
very large. The infrared propagator is then obtained from the quantum field
theory of the scalar field producing a full spectrum. The results are in fully
agreement with recent lattice computations. We get a finite propagator at zero
momentum, the ghost propagator going to infinity as with
.Comment: 7 pages, no figure. After proofs correction. To appear in Physics
Letters
A strongly perturbed quantum system is a semiclassical system
We show that a strongly perturbed quantum system, being a semiclassical
system characterized by the Wigner-Kirkwood expansion for the propagator, has
the same expansion for the eigenvalues as for the WKB series. The perturbation
series is rederived by the duality principle in perturbation theory.Comment: 4 pages, no figures. Accepted for publication in Proceedings of the
Royal Society
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