Symplectic quantization of the BF gravity in 1+1 dimensions

This paper analyzes the symplectic structure and path integral quantization of [Formula: see text]-dimensional Background-Field (BF) theory, primarily focused on the study of gravity in two dimensions. We employ the Faddeev–Jackiw symplectic method, further enhanced by the contributions of Barcelos-Neto and Wotzasek. As a gauge theory, the BF model exhibits a distinct pre-symplectic geometry characterized by a fiber bundle, which is the local product of a regular phase space and the Lie algebra generated by the null vectors of the pre-symplectic 2-form. We investigate two gauge choices and perform path integral quantization as a natural consequence of establishing a quasi-proper symplectic structure for each gauge fixing.