Batalin-Vilkovisky quantization of symmetric Chern-Simons theory

We study the manifestly covariant three-dimensional symmetric ChernSimons action in terms of the Batalin-Vilkovisky quantization method. We find that the Lorentz covariant gauge fixed version of this action is reduced to the usual Chern-Simons type action after a proper field redefinition. Furthermore, the renormalizability of the symmetric Chern-Simons theory turns out to be the same as that of the original Chern-Simons theory. electronic address: [email protected] electronic address: [email protected] electronic address: [email protected] 1 Chern-Simons(CS) theory [1] has been studied in various arena. The key structure which gives interesting phenomena is due to the unusual commutator between the gauge fields, which is essentially arisen from the Dirac method for the quantization of second class constraint system [2]. On the other hand, the second class constraint system can be in principle converted into the first class constraint system by use of the Batalin-Fradkin-Tyutin(BFT) method [3] in the Hamiltonian formalism. The resulting first class constraint system is invariant with respect to the local symmetry implemented by the first class constraints. A few years ago, the second class constraint of the CS theory coupled to some complex fields was converted into first class one in the BFT Hamiltonian method [4], and subsequently straight forward non-Abelian extension was performed [5]. However, the Wess-Zumino like action to convert the second class system into first class one in the Lagrangian formulation depends on the content of matter couplings, and general covariance is unfortunately lost. Recently, the manifestly covariant symmetric CS action has been obtained [6]. The newly obtained one has only first class constraints unlike the usual one which has both first class constraints and second class constraints. The symmetric CS theory can be obtained by simply substituting the original gauge field in the CS action with the infinite sum of newly introduced auxiliary vector fields [6]. Note that at first sight, the appearance of the resulting symmetric CS action seems to be the same form as the original CS action, however, it is nonlocal in that the infinite series of auxiliary fields are involved in the symmetric action. Of course, in the unitary gauge, the original local CS action is reproduced. On the other hand, the Abelian CS theory coupled to the complex matter fields was reconsidered in [6] as a physical application, which is essentially first class constraint system. By analyzing this model without any gauge fixing condition, one can naturally obtain gaugeindependent anyon operators which are also free from path-ordering problems between field operators. Therefore, in the symmetric formulation, the construction of anyon operator is simply realized in the gauge-independent way without any ordering problems. In this paper, we study the symmetric CS action which has full symmetries by use of the Batalin-Vilkovisky(BV) [7] quantization method, and show the equivalence between the 2 symmetric CS action and the original CS action. We find that the gauge fixed version of this action turns out to be the same as the usual Chern-Simons type after a proper field redefinition. Furthermore, the renormalizability program turns out to be the same as that of the original Chern-Simons theory. We now first recapitulate the gauge structure of the non-Abelian CS theory. The CS action with fully first class constraints is given as SSCS = κ ∫