Classical ChernSimons theory, Part 1
Abstract
There is a large mathematical literature on classical mechanics and field theory, especially on the relationship to symplectic geometry. One might think that the classical ChernSimons theory, which is topological and so has vanishing hamiltonian, is completely trivial. However, this theory exhibits interesting geometry that is usually absent from ordinary field theories. (The same is true on the quantum level; topological quantum field theories exhibit geometric properties not usually seen in ordinary quantum field theories, and they lack analytic properties which are usually seen.) In this paper we carefully develop this geometry. Of particular interest are the line bundles with connection over the moduli space of flat connections on a 2manifold. We extend the usual theory to cover 2manifolds with boundary. We carefully develop ``gluing laws'' in all of our constructions, including the line bundle with connection over moduli space. The corresponding quantum gluing laws are fundamental. Part 1 covers connected and simply connected gauge groups; Part 2 will cover arbitrary compact Lie groups.
 Publication:

arXiv eprints
 Pub Date:
 June 1992
 arXiv:
 arXiv:hepth/9206021
 Bibcode:
 1992hep.th....6021F
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Quantum Algebra
 EPrint:
 60 pages. This paper is written using AMSTeX 2.1, which can be obtained via ftp from the American Mathematical Society (instructions included)