Related papers: Chern-Simons Theory, Vassiliev Invariants, Loop Qu…
An exposition of Vassiliev invariants is given in terms of the simplest approach to the functional integral construction of link invariants from Chern-Simons theory. This approach gives the top row evaluations of Vassiliev invariants for…
We study Chern-Simons Gauge Theory in axial gauge on ${\mathbb R}^3.$ This theory has a quadratic Lagrangian and therefore expectations can be computed nonperturbatively by explicit formulas, giving an (unbounded) linear functional on a…
Recent work on the loop representation of quantum gravity has revealed previously unsuspected connections between knot theory and quantum gravity, or more generally, 3-dimensional topology and 4-dimensional generally covariant physics. We…
A new approach to the quantization of Chern-Simons theory has been developed in recent papers of the author. It uses a "simulation" of the moduli space of flat connections modulo the gauge group which reveals to be related to a lattice…
A brief review of the development of Chern-Simons gauge theory since its relation to knot theory was discovered in 1988 is presented. The presentation is done guided by a dictionary which relates knot theory concepts to quantum field theory…
While general quantum field theories (QFTs) have yet to be rigorously defined in mathematics, they have generated new mathematics and have served as a unifying principle connecting different branches of the subject. In 1989, Witten made a…
This paper is an exposition of heuristics related to Witten's functional integral, relating it to Vassiliev invariants and to the Kontsevich integrals that can be used to produce Vassiliev invariants of knots and links.In particular, we…
A brief review on the progress made in the study of Chern-Simons gauge theory since its relation to knot theory was discovered ten years ago is presented. Emphasis is made on the analysis of the perturbative study of the theory and its…
I argue that the complete partition function of 3D quantum gravity is given by a path integral over gauge-inequivalent manifolds times the Chern-Simons partition function. In a discrete version, it gives a sum over simplicial complexes…
Chern-Simons gauge theory, since its inception as a topological quantum field theory, has proved to be a rich source of understanding for knot invariants. In this work the theory is used to explore the definition of the expectation value of…
We analyse the structure of the perturbative series expansion of Chern-Simons gauge theory in the light-cone gauge. After introducing a regularization prescription that entails the consideration of framed knots, we present the general form…
The title of this article refers to analytic continuation of three-dimensional Chern-Simons gauge theory away from integer values of the usual coupling parameter k, to explore questions such as the volume conjecture, or analytic…
The expectation value of a Wilson loop in a Chern--Simons theory is a knot invariant. Its skein relations have been derived in a variety of ways, including variational methods in which small deformations of the loop are made and the changes…
We consider the $U(1)$ Chern-Simons gauge theory defined in a general closed oriented 3-manifold $M$; the functional integration is used to compute the normalized partition function and the expectation values of the link holonomies. The…
On the fiftieth anniversary of Yang-Mills theory, I review the contribution to its understanding by my collaborators and me. Contents: 1.Gauge Theories and Quantum Anomalies; 2.Mathematical Connections; 3. Gauge Field Dynamics other than…
A brief introduction to Topological Quantum Field Theory as well as a description of recent progress made in the field is presented. I concentrate mainly on the connection between Chern-Simons gauge theory and Vassiliev invariants, and…
We present an implementation of the loop representation of quantum gravity on a square lattice. Instead of starting from a classical lattice theory, quantizing and introducing loops, we proceed backwards, setting up constraints in the…
In the late 1980s Witten used the Chern-Simons form of a connection to construct new invariants of 3-manifolds and knots, recovering in particular the Jones invariants. Since then the associated topological quantum field theory (TQFT) has…
We generalize the idea of Vassiliev invariants to the spin network context, with the aim of using these invariants as a kinematical arena for a canonical quantization of gravity. This paper presents a detailed construction of these…
We provide a necessary and sufficient condition for the consistency of the supertrace, through the existence of a certain ground state projector. We build this projector and check its properties to the first two orders in the number…