Related papers: Non-covariance of the generalized holonomies: Exam…
It has been pointed out that the holonomy of generic extended loops is not gauge covariant. We show how to define a family of extended loops for which previous criticism does not apply. We also give sufficient conditions that extended loops…
Holonomy algebras arise naturally in the classical description of Yang-Mills fields and gravity, and it has been suggested, at a heuristic level, that they may also play an important role in a non-perturbative treatment of the quantum…
In this paper we continue the development of Quantum Holonomy Theory, which is a candidate for a fundamental theory, by constructing separable strongly continuous representations of its algebraic foundation, the quantum…
Important characteristics of the loop approach to quantum gravity are a specific choice of the algebra A of observables and of a representation of A on a measure space over the space of generalized connections. This representation is…
The Gauss constraint in the extended loop representation for quantum gravity is studied. It is shown that there exists a sector of the state space that is rigorously gauge invariant without the generic convergence issues of the extended…
We consider two simple criteria for when a physical theory should be said to be "generally covariant", and we argue that these criteria are not met by Yang-Mills theory, even on geometric formulations of that theory. The reason, we show, is…
We point out an incompleteness of formulations of gravitational and gauge theories that use traces of holonomies around closed curves as their basic variables. It is shown that in general such loop variables have to satisfy certain…
We use twist deformation techniques to analyse the behaviour under area-preserving diffeomorphisms of quantum averages of Wilson loops in Yang-Mills theory on the noncommutative plane. We find that while the classical gauge theory is…
We review the application of the loop representation to gauge theories and general relativity. The emphasis lies on exhibiting the loop calculus techniques, and their application to the canonical quantization. We discuss the role that knot…
In this paper, we present a non-geometrodynamic quantum Yang-Mills theory of gravity based on the homogeneous Lorentz group within the general framework of the Poincare gauge theories. The obstacles of this treatment are that first, on the…
A four dimensional generally covariant field theory is presented which describes non-dynamical three geometries coupled to scalar fields. The theory has an infinite number of physical observables (or constants of the motion) which are…
We present a 4-dimensional generally covariant gauge theory which leads to the Gauss constraint but lacks both the Hamiltonian and spatial diffeomorphism constraints. The canonical theory therefore resembles Yang-Mills theory without the…
As a canonical and generally covariant gauge theory, loop quantum gravity requires special techniques to derive effective actions or equations. If the proper constructions are taken into account, the theory, in spite of considerable…
In generalized Yang-Mills theories scalar fields can be gauged just as vector fields in a usual Yang-Mills theory, albeit it is done in the spinorial representation. The presentation of these theories is aesthetic in the following sense: A…
We review some attempts of reformulating both gauge theory and general relativity in terms of holonomy-dependent loop variables. The emphasis lies on exhibiting the underlying mathematical structures, which often are not given due attention…
Since the gauge group underlying 2+1-dimensional general relativity is non-compact, certain difficulties arise in the passage from the connection to the loop representations. It is shown that these problems can be handled by appropriately…
An equation for the quantum average of the gauge invariant Wilson loop in non-commutative Yang-Mills theory with gauge group U(N) is obtained. In the 't Hooft limit, the equation reduces to the loop equation of ordinary Yang-Mills theory.…
We recall the non-Abelian Stokes theorem for the Wilson loop in the Yang-Mills theory and discuss its meaning. Then we move to `gravitational Wilson loops', i.e. to holonomies in curved d=2,3,4 spaces and derive non-Abelian Stokes theorems…
The equations of motion of quantum Yang - Mills theory (in the planar `large N' limit), when formulated in Loop-space are shown to have an anomalous term, which makes them analogous to the equations of motion of WZW models. The anomaly is…
A modification of the gauge theory is proposed, in which the set of generalized coordinates is supplemented with symmetry transformation parameters, and a condition is additionally imposed on the latter that ensures the classical character…