Functional quantization of Generalized Scalar Duffin-Kemmer-Petiau Electrodynamics


Abstract in English

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 Diracs methodology by determining the Hamiltonian transition amplitude. In particular, the covariant transition amplitude is established in the generalized non-mixing Lorenz gauge. The complete Greens functions are obtained through functional methods and the theorys renormalizability is also detailed presented. Next, the radiative corrections for the Greens 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.

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