# Gauge-invariant approach to quark dynamics

Abstract : The main aspects of a gauge-invariant approach to the description of quark dynamics in the nonperturbative regime of QCD are first reviewed. In particular, the role of the parallel transport operation in constructing gauge-invariant Green's functions is presented, and the relevance of Wilson loops for the representation of the interaction is emphasized. Recent developments, based on the use of polygonal lines for the parallel transport operation, are then presented. An integro-differential equation is obtained for the quark Green's function defined with a phase factor along a single, straight line segment. It is solved exactly and analytically in the case of two-dimensional QCD in the large $N_c$ limit. The solution displays the dynamical mass generation phenomenon for quarks, with an infinite number of branch-cut singularities that are stronger than simple poles.
Document type :
Journal articles

http://hal.in2p3.fr/in2p3-01234636
Contributor : Sophie Heurteau <>
Submitted on : Friday, November 27, 2015 - 10:58:16 AM
Last modification on : Monday, June 29, 2020 - 6:24:20 PM

### Citation

H. Sazdjian. Gauge-invariant approach to quark dynamics. Frontiers of Physics, Springer, 2016, 11 (1), pp.111101. ⟨10.1007/s11467-015-0515-8⟩. ⟨in2p3-01234636⟩

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