1,219 research outputs found
Chern-Simons Gauge Theory: Ten Years After
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 connection to the theory of Vassiliev invariants. It is described how the
study of the quantum field theory for three different gauge fixings leads to
three different representations for Vassiliev invariants. Two of these gauge
fixings lead to well known representations: the covariant Landau gauge
corresponds to the configuration space integrals while the non-covariant
light-cone gauge to the Kontsevich integral. The progress made in the analysis
of the third gauge fixing, the non-covariant temporal gauge, is described in
detail. In this case one obtains combinatorial expressions, instead of integral
ones, for Vassiliev invariants. The approach based on this last gauge fixing
seems very promising to obtain a full combinatorial formula. We collect the
combinatorial expressions for all the Vassiliev invariants up to order four
which have been obtained in this approach.Comment: 62 pages, 21 figures, lecture delivered at the workshop "Trends in
Theoretical Physics II", Buenos Aires, November 199
Kontsevich integral for knots and Vassiliev invariants
We review quantum field theory approach to the knot theory. Using holomorphic
gauge we obtain the Kontsevich integral. It is explained how to calculate
Vassiliev invariants and coefficients in Kontsevich integral in a combinatorial
way which can be programmed on a computer. We discuss experimental results and
temporal gauge considerations which lead to representation of Vassiliev
invariants in terms of arrow diagrams. Explicit examples and computational
results are presented.Comment: 25 pages, 17 figure
Vassiliev invariants: a new framework for quantum gravity
We show that Vassiliev invariants of knots, appropriately generalized to the
spin network context, are loop differentiable in spite of being diffeomorphism
invariant. This opens the possibility of defining rigorously the constraints of
quantum gravity as geometrical operators acting on the space of Vassiliev
invariants of spin nets. We show how to explicitly realize the diffeomorphism
constraint on this space and present proposals for the construction of
Hamiltonian constraints.Comment: 15 pages, several figures included with psfi
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