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 α-order; and, as it turns out, an unexpected m Pdependent 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 α 2 -order, where is observed contributions from the meson selfenergy 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 ≤ k 2 < m 2 P . It is also shown in our final discussion that the new divergence is absorbed suitably by the mass counter-term δ Z0 , showing therefore that the gauge WFT identities are satisfied still.

Renormalization of generalized scalar Duffin-Kemmer-Petiau electrodynamics

“…However, remarkably, this divergence is absorbed by the mass counterterm δ Z 1 , clearly at equation (6.18), showing therefore that the WFT identity (4.4) is satisfied at this order. A similar situation was also found in the GSQED 4 [48].…”

“…The previous result is consistent with relativistic covariance and the Ward-Fradkin-Takahashi identity, as in (4.8). The comparison between (6.5) and the known result in GSQED 4 [48] leads to the conclusion that they are the same.…”

“…fields in a different phenomenologically way, which will certainly complement the known results in the literature [21,48]. This work is therefore devoted to the analysis of the Generalized Scalar Duffin-Kemmer-Petiau Electrodynamics.…”

Reduced Order Podolsky Model

“…Due to its generality appeal, the understanding of higher-order theories constitutes a fascinating challenge to physicists and mathematicians. In particular, recently, Podolsky's generalized electrodynamics has been revisited and scrutinized in its various aspects in a handful of papers [4,5,6,7,8,9], establishing a lively rich discussion on the subject. The model may be used as an effective theory itself or as a smaller component of more elaborated ones.…”

A conducting surface in Lee–Wick electrodynamics

“…Since its proposal, the theory has been standing out by its classical as well as its quantum aspects, as it exhibits many interesting peculiarities. We can mention, for instance, the fact that in this electrodynamics the self-energy of a point charge is finite in 3 + 1 dimensions [7][8][9][10][11][12], a Dirac string can produce a magnetic field [7], it stem a finite theory closely related to the Pauli-Villars regularization scheme [5,8,[13][14][15][16][17][18] where the divergences of the quantum electrodynamics are controllable [19][20][21] and it exhibits classical dynamical stability [22]. These features have made the model a widely studied subject in a variety of scenarios, mainly regarding its extension to the Standard Model [14,16,18,[23][24][25][26][27][28][29][30][31][32][33][34][35][36][37].…”