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 ($GSQE{D}_4$). 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 $m^2\le k^2<m_P^2$. 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.

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• BRST symmetry and fictitious parameters
• Reduced Order Podolsky Model
• Stability and consistent interactions in Podolsky's generalized electrodynamics
• Path Integral Quantization of Generalized Stueckelberg Electrodynamics: A Faddeev-Jackiw Approach
• Thermal effective Lagrangian of generalized electrodynamics in static gravitational fields
• Construction of consistent interactions in higher derivative Yang-Mills gauge theory with matter fields