Gauge Invariant Quark Green Research Articles

On the role of dynamical quark mass generation in chiral symmetry breaking in QCD

The phenomenon of dynamical quark mass generation is studied in QCD within the framework of a gauge invariant formalism. An exact relationship is established between the equation satisfied by the scalar part of the two-point gauge invariant quark Green's function and the quark-antiquark bound state equation in the chiral limit. A possible nontrivial solution of the former yields a massless pseudoscalar solution of the bound state equation with vanishing total momentum. The result is also corroborated by the corresponding Ward-Takahashi identity. The problem is explicitly solved in two-dimensional QCD in the large-Nc limit.

Two-point gauge invariant quark Green's functions with polygonal phase factor lines

Polygonal lines are used for the paths of the gluon field phase factors entering in the definition of gauge invariant quark Green's functions. This allows classification of the Green's functions according to the number of segments the polygonal lines contain. Functional relations are established between Green's functions with polygonal lines with different numbers of segments. An integrodifferential equation is obtained for the quark two-point Green's function with a path along a single straight line segment where the kernels are represented by a series of Wilson loop averages along polygonal contours. The equation is exactly and analytically solved in the case of two-dimensional QCD in the large-Nc limit. The solution displays generation of an infinite number of dynamical quark masses accompanied with branch point singularities that are stronger than simple poles. An approximation scheme, based on the counting of functional derivatives of Wilson loops, is proposed for the resolution of the equation in four dimensions.

Gauge invariant bound state equations for quark-antiquark systems in QCD

Using gauge invariant quark Green's functions, defined with path-ordered gluon field phase factors along polygonal lines, and functional relations among them, two compatible bound state equations of the Dirac type are established for quark-antiquark systems, each relative to the quark or to the antiquark of the system. The kernels of the bound state equations are defined through a series of Wilson loop averages along closed polygonal contours and their functional derivatives on them. A sufficient criterion for spontaneous chiral symmetry breaking is derived, relating the Goldstone boson wave function in the zero total momentum limit with the scalar part of the gauge invariant quark two-point Green's function.

Structure of the Gauge Invariant Quark Green’s Function in QCD2

We study, in two-dimensional QCD and in the large-N c limit, the properties of the gauge invariant quark Green’s function, defined with a path-ordered phase factor along a straight line. The analysis is done by means of an exact integrodifferential equation. The Green’s function is found to be infrared finite, with singularities represented by an infinite number of threshold type branch points with a power −3/2, starting at positive mass squared values. Its expression is analytically determined.

Properties of the gauge invariant quark Green's function in two-dimensional QCD

Using an exact integrodifferential equation we study the properties of the gauge invariant quark Green's function, defined with a path-ordered gluon field phase factor along a straight line, in two-dimensional QCD in the large-N_c limit. The Green's function is found to be infrared finite with singularities represented by an infinite number of threshold type branch points with a power equal to -3/2, starting at positive mass squared values. The solution is analytically determined.

Spectral properties of the gauge invariant quark Green’s function in two-dimensional QCD

The gauge invariant quark Green's function with a path-ordered phase factor along a straight-line is studied in two-dimensional QCD in the large-Nc limit by means of an exact integrodifferential equation. Its spectral functions are analytically determined. They are infra-red finite and lie on the positive real axis of the complex plane of the momentum squared variable, corresponding to momenta in the forward light cone. Their singularities are represented by an infinite number of threshold type branch points with power-law -3/2, starting at positive mass values, characterized by an integer number n and increasing with n. The analytic expression of the Green's function for all momenta is presented. The appearance of strong threshold singularities is suggestive of the fact that quarks could not be observed as asymptotic states.

Integral equation for gauge invariant quark two-point Green’s function in QCD

Gauge invariant quark two-point Green's functions defined with path-ordered gluon field phase factors along skew-polygonal lines joining the quark to the antiquark are considered. Functional relations between Green's functions with different numbers of path segments are established. An integral equation is obtained for the Green's function defined with a phase factor along a single straight line. The equation implicates an infinite series of two-point Green's functions, having an increasing number of path segments; the related kernels involve Wilson loops with contours corresponding to the skew-polygonal lines of the accompanying Green's function and with functional derivatives along the sides of the contours. The series can be viewed as an expansion in terms of the global number of the functional derivatives of the Wilson loops. The lowest-order kernel, which involves a Wilson loop with two functional derivatives, provides the framework for an approximate resolution of the equation.