Geodesic
Equation for the quark propagator in~the infrared region and some properties of~its solutions
Teoretičeskaâ i matematičeskaâ fizika, Tome 85 (1990) no. 1, pp. 54-63

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The Schwinger–Dyson equation for the quark propagator in the infrared region is considered. The infrared asymptotic behavior $D(k)\sim M^2/(k^2)^2$ of the gluon propagator in the covariant gauge is used, and solutions are constructed for different regularizations of the singularity of this propagator. A nonperturbative solution, nonanalytic in the coupling constant, is obtained in a special case; in the ultraviolet region it tends exponentially to the free quark propagator. The solution contains two parameters, one of which corresponds to breaking of chiral symmetry, while the other can be fixed by means of the chiral limit. As a result, a solution free of singularities with respect to the momentum is obtained. 
@article{TMF_1990_85_1_a5,
     author = {A. I. Davydychev},
     title = {Equation for the quark propagator in~the infrared region and some properties of~its solutions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {54--63},
     publisher = {mathdoc},
     volume = {85},
     number = {1},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1990_85_1_a5/}
}
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A. I. Davydychev. Equation for the quark propagator in~the infrared region and some properties of~its solutions. Teoretičeskaâ i matematičeskaâ fizika, Tome 85 (1990) no. 1, pp. 54-63. http://geodesic.mathdoc.fr/item/TMF_1990_85_1_a5/