Dirac quantization of Chern-Simons theories in (2+1) dimensions

Abstract

The authors quantize the Abelian and nonAbelian Chern-Simons theories in (2+1) dimensions by the Dirac quantization formulation. Gauge theories with a topological mass term in both the Abelian and nonAbelian cases are also quantized by the same method.

Geometric quantization of topological gauge theories

“…The result above is also in agreement with the work of ref. [9]. Considering now the Coulomb gauge, the brackets just involving A i and π j are…”

“…A manifest covariant canonical quantization was carried out more recently [6] and also the quantization by means of operator formalism [7]. The canonical quantization based on the Dirac Hamiltonian procedure [8] was developed by Lin and Ni [9], using the temporal gauge, and Martínez-Fernándes and Wotzasek [10], using the Coulomb gauge.…”

Kβ X-Ray Emission Band and K X-Ray Absorption-Edge Structure of Sulfur in Layered Transition-Metal Compounds TiS2, ZrS2and HfS2

“…Gauge theories in (2 + 1) dimensions involving the Chern-Simons (CS) term coupled to matter fields describe excitations with fractional statistics (for a comprehensive review see, for example, [1] and references therein, [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]). Such studies form a broad field [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18].…”

“…This necessitates the present study. Also, different aspects of this theory have been studied by several authors in various contexts [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. For further details of the motivation for a study of the different aspects of CS theories by various authors, including a comparative description of different studies, we refer to our earlier work [16][17][18].…”

Quantization of Chern-Simons field theory in the Coulomb gauge

“…In the first part of the talk the C-S field theories are analysed by means of the Dirac's formalism for constrained systems. Besides some subtleties already noticed in 24 , the derivation of the final Dirac brackets requires in the Coulomb gauge some care with distributions. Moreover, the final commutation relations (CR's) between the fields are derived both in the case of pure and interacting C-S field theories.…”