Type of Work

Article

Date

6-1999

Journal Title

Nuclear Physics B

Journal ISSN

0550-3213

Journal Volume

550

Journal Issue

3

First Page

531

Last Page

560

DOI

10.1016/S0550-3213(99)00164-9

Abstract

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 a network of Wilson lines — an embedded graph invariant. Using a generalization of the variational method, lowest-order results for invariants for graphs of arbitrary valence and general vertex tangent space structure are derived. Gauge invariant operators are introduced. Higher order results are found. The method used here provides a Vassiliev-type definition of graph invariants which depend on both the embedding of the graph and the group structure of the gauge theory. It is found that one need not frame individual vertices. However, without a global projection of the graph there is an ambiguity in the relation of the decomposition of distinct vertices. It is suggested that framing may be seen as arising from this ambiguity — as a way of relating frames at distinct vertices.

Notes

This document is the publisher's version of an article published in:

Nuclear Physics B., vol. 550, no. 3(1999): 531-560. doi: 10.1016/S0550-3213(99)00164-9

Hamilton Areas of Study

Physics