Functional quantization of Generalized Scalar Duffin-Kemmer-Petiau Electrodynamics

TL;DR

This paper systematically quantizes and analyzes the quantum properties of Generalized Scalar Duffin-Kemmer-Petiau Electrodynamics, revealing novel divergences and demonstrating the renormalization process within the theory.

Contribution

It provides a detailed quantization, Green's functions, and renormalization analysis of GSDKP, including the discovery of an unexpected divergence in the DKP sector.

Findings

Identified an unexpected $m_{P}$-dependent divergence in the DKP sector.

Demonstrated the renormalizability of GSDKP through diagrammatic analysis.

Established an energy range where the theory is well-defined.

Abstract

The main goal of this work is to study systematically the quantum aspects of the interaction between scalar particles in the framework of Generalized Scalar Duffin-Kemmer-Petiau Electrodynamics (GSDKP). For this purpose the theory is quantized after a constraint analysis following Dirac's methodology by determining the Hamiltonian transition amplitude. In particular, the covariant transition amplitude is established in the generalized non-mixing Lorenz gauge. The complete Green's functions are obtained through functional methods and the theory's renormalizability is also detailed presented. Next, the radiative corrections for the Green's functions at $\alpha $-order are computed; and, as it turns out, an unexpected $m_{P}$-dependent divergence on the DKP sector of the theory is found. Furthermore, in order to show the effectiveness of the renormalization procedure on the present theory, a diagrammatic discussion on the photon self-energy and vertex part at $\alpha ^{2}$-order are presented, where it is possible to observe contributions from the DKP self-energy function, and then analyse whether or not this novel divergence propagates to higher-order contributions. Lastly, an energy range where the theory is well defined: $m^{2}\ll k^{2}<m_{p}^{2}$ was also found by evaluating the effective coupling for the GSDKP.