Manifestly covariant action for symmetric Chern-Simons field theory

We study a three-dimensional symmetric Chern-Simons field theory with a general covariance and it turns out that the original Chern-Simons theory is just a gauge fixed action of the symmetric Chern-Simons theory whose constraint algebra belongs to fully first class constraint system. The Abelian Chern-Simons theory with matter coupling is studied for the construction of anyon operators without any ordering ambiguity with the help of this symmetric Chern-Simons action. Finally we shall discuss some connections between the present symmetric formulation of Chern-Simons theory and the Stükelberg mechanism. PACS numbers:11.10.Ef, 11.10.Kk, 11.15.-q electronic address:[email protected] electronic address: [email protected] 1