Related papers: Non-Abelian Stokes Theorems in Yang-Mills and Grav…

We present the non-Abelian Stokes theorem for the Wilson loop in various forms and discuss its meaning. Its validity has been recently questioned by Faber, Ivanov, Troitskaya and Zach. We demonstrate that all points of their criticism are…

It is proposed an integral formulation of classical Yang-Mills equations in the presence of sources, based on concepts in loop spaces and on a generalization of the non-abelian Stokes theorem for two-form connections. The formulation leads…

We derive a new version of the non-Abelian Stokes theorem for the Wilson loop in the SU(N) case by making use of the coherent state representation on the coset space $SU(N)/U(1)^{N-1}=F_{N-1}$, the flag space. We consider the SU(N)…

We give a gauge-independent definition of magnetic monopoles in the $SU(N)$ Yang-Mills theory through the Wilson loop operator. For this purpose, we give an explicit proof of the Diakonov-Petrov version of the non-Abelian Stokes theorem for…

A formula constituting the non-Abelian Stokes theorem for general semi-simple compact gauge groups is presented. The formula involves a path integral over a group space and is applicable to Wilson loop variables irrespective of the topology…

We derive a new version of SU(3) non-Abelian Stokes theorem by making use of the coherent state representation on the coset space $SU(3)/(U(1)\times U(1))=F_2$, the flag space. Then we outline a derivation of the area law of the Wilson loop…

We present a review of gravitating particle-like and black hole solutions with non-Abelian gauge fields. The emphasis is given to the description of the structure of the solutions and to the connection with the results of flat space soliton…

It is shown that the application of the non-Abelian Stokes theorem to the computation of the operators constructed with Wilson loop will lead to ambiguity, if the gauge field under consideration is a non-trivial one. This point is…

We derive a new non-abelian Stokes theorem by rewriting the Wilson loop as a gauge-invariant area integral, at the price of integrating over an auxiliary field from the coset SU(N) / [U(1)]^{N-1} space. We then introduce the relativistic…

Finding diffeomorphism-invariant observables to characterize the properties of gravity and spacetime at the Planck scale is essential for making progress in quantum gravity. The holonomy and Wilson loop of the Levi-Civita connection are…

In this short review main issues related to the non-Abelian Stokes theorem have been addressed. The two principal approaches to the non-Abelian Stokes theorem, operator and two variants (coherent-state and holomorphic) of the path-integral…

A key aspect of a recent proposal for a {\em generalized loop representation} of quantum Yang-Mills theory and gravity is considered. Such a representation of the quantum theory has been expected to arise via consideration of a particular…

We write down the Yang-Mills partition function and the average Wilson loop in terms of local gauge-invariant variables being the six components of the metric tensor of dual space. The Wilson loop becomes the trace of the parallel…

We present non-perturbative results for U(1) gauge theory in spaces, which include a non-commutative plane. In contrast to the commutative space, such gauge theories involve a Yang-Mills term, and the Wilson loop is complex on the…

We describe a finite analogue of the Poisson algebra of Wilson loops in Yang-Mills theory. It is shown that this algebra arises in an apparently completely different context; as a Lie algebra of vector fields on a non-commutative space.…

We investigate the temporal Wilson loop using the Hamiltonian approach to Yang-Mills theory. In simple cases such as the Abelian theory or the non-Abelian theory in (1+1) dimensions, the known results can be derived using unitary…

We show that the Wilson loop operator for SU(N) Yang-Mills gauge connection is exactly rewritten in terms of conserved gauge-invariant magnetic and electric currents through a non-Abelian Stokes theorem of the Diakonov-Petrov type. Here the…

We formulate the canonical structure of Yang--Mills theory in terms of Poisson brackets of gauge invariant observables analogous to Wilson loops. This algebra is non--trivial and tractable in a light--cone formulation. For U(N) gauge…

We provide a method and the results for the calculation of the holonomy of a Yang-Mills connection in an arbitrary triangular path, in an expansion (developed here to fifth order) in powers of the corresponding segments. The results might…

We investigate the temporal Wilson loop using the Hamiltonian approach to Yang-Mills theory. In simple cases such as the Abelian theory or the non-Abelian theory in (1+1) dimensions, the known results can be reproduced using unitary…