The BF formalism for QCD and quark confinement

Abstract

Using the BF version of pure Yang-Mills, it is possible to find a covariant representation of the 't Hooft magnetic flux operator. In this framework, 't Hooft's pioneering work on confinement finds an explicit realization in the continuum. Employing the Abelian projection gauge we compute the expectation value of the magnetic variable and find the expected perimeter law. We also check the area law behaviour for the Wilson loop average and compute the string tension which turns out to be of the right order of magnitude.

Remarks on monopoles in Abelian projected continuum Yang-Mills theories

“…We proceed by rewriting the term TrF µν F µν in a first order formalism by introducing an antisymmetric two-form field B µν [8,9] Tr 1 4…”

Dimension of the Moduli Space and Hamiltonian Analysis of Bf Field Theories

“…The BF formalism [1,2,3] in arbitrary space or space-time dimensions has shown profound relationships between topological field theory and quantum field theory, from a simplified version of general relativity [4,5], to a new formulation of Yang-Mills (YM) theory [6,7,8,9,10,11]. In the so called first-order formulation, YM theory can be viewed as a perturbative expansion in the coupling constant g around the pure topological BF theory; additionally the BF first-order formulation is on shell equivalent to the usual (second-order) YM theory.…”

2-Step Growth Method and Microcrystalline Silicon Thin Film Solar Cells Prepared by Hot Wire Cell Method

“…On the other hand, the Yang-Mills gauge theory has recently been re-interpreted as a deformation of a pure BF theory [2,3,4,5,6]. In its "extended" version [5], this BF-Yang-Mills (BFYM) theory is described by the action Σ BFYM = d n x ε µ 1 ...µn B a µ 1 ...µ n−2 F a µ n−1 µn + B a µ 1 ...µ n−2 + D [µ 1 η a µ 2 ...µ n−2 ] 2 , (1.1)…”