Duality and self-duality of the spin-1 model in the covariant operator formalism

Abstract

Abstract We perform the covariant operator quantization of the spin-$1$ model in $2+1$ spacetime dimensions to rigorously establish its dualities. For this purpose, the Kugo–Ojima–Nakanishi formalism, based on an indefinite metric Hilbert space in the Heisenberg picture, is used. We show that it is possible to extract a massive physical excitation constructed from a linear combination of the vector field $A_{\mu}$ and the $B$-field. In turn, we also show that this excitation generates the Maxwell–Chern–Simons theory. This is achieved by exploring the two-point function of the vector field.