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

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 Aμ 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.