Feynman Rules for Electromagnetic and Yang-Mills Fields from the Gauge-Independent Field-Theoretic Formalism

Hedgehogs in Wilson loops and phase transition in SU(2) Yang–Mills theory

“…In YM theory, the hedgehog loop is classified by the pair of numbers (z, n), where z = ±1 is the central element of the Wilson loop W C ∈ Z 2 determined by Eq. (5) and n is the winding number associated with hedgehogs structure (6). Below, we call z the "center charge" of the hedgehog loop.…”

“…Mathematically, these loops are as good as the gauge fields from the standpoint of describing properties (in particular, nonperturbative) of YM theories [6]. Having the importance of the order-parameter (Cooper-pair) field in the Ginzburg-Landau model of superconductivity in mind, we compare the properties of this field with the well-known properties of the Wilson loop General arguments were given in [7] to identify the defect-like trajectories in the Yang-Mills theory with the closed paths in space for which the (untraced) Wilson loop takes its value in the center of the color group.…”

“…On the other hand, YM theory can be entirely formulated [6] in the language of colorless composite fields (Wilson loops), which are traces of the loop functionals of the gluon fields. Mathematically, these loops are as good as the gauge fields from the standpoint of describing properties (in particular, nonperturbative) of YM theories [6].…”

Evolution of light-like Wilson loops with a self-intersection in loop space

“…(4), is a special case of the Fréchet derivative [9,10], the details of which will be discussed elsewhere [11]. In this work, we consider some symmetrical combinations of two quadrilateral Wilson loops on the light-cone, for which we test conjecture (4). Put in a Wilson loop variable language: we are calculating W 1 [Γ], with Γ = Γ 1 Γ 2 , where the product between the loops is defined in generalized loop space [12].…”

“…From this holonomy, which is some N × N matrix in the representation of the gauge group, a gauge invariant variable can be obtained by taking the trace 1 . This trace introduces, however, extra constraints on the loops: the so-called Mandelstam constraints [1][2][3][4], which assure that the product of traces over holonomies is again the trace of a holonomy. Gauge theory can then be represented in a loop space setting, where the observables are now built from the vacuum expectation values of products of traces of holonomies, referred to as Wilson loop variables [2,3,[5][6][7]:…”