Batalin-Fradkin-Vilkovisky quantization of the generalized scalar electrodynamics

Abstract: This work comprises a study upon the quantization and the renormalizability of the generalized electrodynamics of spinless charged particles (mesons), namely, the Generalized Scalar Electrodynamics ($GSQED_{4}$). The theory is quantized in the covariant framework of the Batalin-Fradkin-Vilkovisky method. Thereafter, the complete Green's functions are obtained through functional methods and a proper discussion on the theory's renormalizability is also given. Next, it is presented the computation and further discussion on the radiative correction at $\alpha$-order; and, as it turns out, an unexpected $m_{P}$-dependent divergence on the mesonic sector of the theory is found. Furthermore, in order to show the effectiveness of the renormalization procedure on the present theory it is also shown a diagrammatic discussion on the photon self-energy at $\alpha^{2}$-order, where is observed contributions from the meson self-energy function. Afterwards, we present the expressions of the counter-terms and effective coupling of the theory. Obtaining from the later a energy range where the theory is defined $m^{2} \leq k^{2} < m_{P}^{2}$. It is also shown in our final discussion that the new divergence is absorbed suitably by the mass counter-term $\delta_{Z_{0}}$, showing therefore that the gauge WFT identities are satisfied still.