arXiv 1404.09402014-04-03hep-th

广义标量电动力学的Batalin-Fradkin-Vilkovisky量子化

Batalin-Fradkin-Vilkovisky quantization of the generalized scalar electrodynamics

R. Bufalo, B. M. Pimentel

发表信息：: Physical Review D 88, 065013 (2013)
DOI：: 10.1103/PhysRevD.88.065013

摘要：

本文研究了无自旋带电粒子（介子）的广义电动力学，即广义标量电动力学（$GSQED_{4}$）的量子化和重整化。在Batalin-Fradkin-Vilkovisky方法的协变框架中对该理论进行了量化。在此基础上，利用泛函方法得到了完整的格林函数，并对理论的重整化性进行了适当的讨论。其次，给出了$α$阶辐射修正的计算和进一步讨论;在理论的介子部分发现了一个与$m_{P}$有关的发散.此外，为了说明重整化过程对本理论的有效性，还对$α^{2}$级的光子自能作了图解讨论，其中观察到介子自能函数的贡献。然后给出了理论的反项和有效耦合的表达式。从后者获得理论定义为$m^{2} \leq k^{2} < m_{P}^{2}$的能量范围。在最后的讨论中还表明，新的发散被质量反项$δ_{Z_{0}}$适当地吸收，从而表明规范WFT恒等式仍然是满足的。

英文摘要：

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 $m_{P}$-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 $α^{2}$-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 $δ_{Z_{0}}$, showing therefore that the gauge WFT identities are satisfied still.

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