We demonstrate that the standard Stueckelberg-modified Proca theory (i.e. a massive Abelian 1-form theory) respects the classical gauge and corresponding quantum (anti-)BRST symmetry transformations in any arbitrary dimension of spacetime within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism. We further show that the Stueckelberg formalism gets modified in the two (1+1)-dimensions of spacetime due to a couple of discrete duality symmetries in the theory which turn out to be responsible for the existence of the nilpotent (anti-)co-BRST symmetry transformations corresponding to the nilpotent (anti-)BRST symmetry transformations of our theory. These nilpotent symmetries exist together in the modified version of the two (1+1)-dimensional (2D) Proca theory. We provide the mathematical basis for the modification of the Stueckelberg-technique, the existence of the discrete duality as well as the continuous (anti-)co-BRST symmetry transformations in the 2D modified version of Proca theory.
The Ultraviolet and Infrared Behavior of an Abelian Proca Model From the Viewpoint of a One-Parameter Extension of the Covariant Heisenberg Algebra
最近，在$(D+1)$维Minkowski时空中提出了协变Heisenberg代数的一个单参数扩张，扩张参数为$l$（$l$是一个维数为$[momentum]^{-1}$的非负常数参数）[G. P. de Brito，P. I. C. Caneda，Y. M. P. Gomes，J. T. Guaitolini Junior和V. Nikoofard，协变量子代数中普朗克尺度修改引起的量子引力的有效模型，Adv. High Energy Phys.2017（2017）4768341]。从协变Heisenberg代数的单参数扩张的观点出发，对Abel Proca模型进行了重新表述。结果表明，上述修正Proca模型的自由空间解满足修正色散关系$\frac{\textbf{p}^2}{\left(1+\frac{Λ^2}{2\hbar^2}\textbf{p}^2\right)^2}=m^2c^2$，其中$Λ=\hbar l$为模型的特征长度尺度.这个修正的色散关系描述了两个有效质量为${\cal M}_{_\pm}(Λ)=\frac{2m}{1\mp\sqrt{1-2\left(\frac{mcΛ}{\hbar}\right)^2}}$的大质量矢量粒子。数值估计表明，在四维时空中，$Λ$的最大值接近于电弱长度尺度，即，$Λ_{_{max}}\sim l_{_{electroweak}}…
BRST Quantization of the Proca Model based on the BFT and the BFV Formalism
Abel Proca模型的BRST量化使用Batalin-Fradkin-Tybern和Batalin-Fradkin-Vilkovisky形式主义来执行。首先，应用BFT哈密顿方法，通过引入新的场，系统地将模型的第二类约束系统转化为有效的第一类约束系统。在求对合哈密顿量时，我们采用了一种新的方法，这种方法比通常的方法简单。我们还表明，在我们的模型中，在原来的第二类约束系统的相空间变量的狄拉克括号是完全相同的泊松括号中相应的修改字段在扩展相空间由于线性字符的约束比较狄拉克或Faddeev-Jackiw形式主义。然后，根据BFV形式，我们得到的理想结果保持BRST对称性的拉格朗日在标准的局域规范固定程序自然包括Stückelberg标量的显式规范对称性破缺效应，由于质量项的存在。分析了非标准非局部规范固定过程。
A Modified Method for Deriving Self-Conjugate Dirac Hamiltonians in Arbitrary Gravitational Fields and Its Application to Centrally and Axially Symmetric Gravitational Fields
Leibniz University Hannover（汉诺威莱布尼茨大学）；Max Planck Institute for Gravitational Physics, Albert Einstein Institute（马克斯·普朗克引力物理研究所，爱因斯坦研究所）；Center for Physical Sciences and Technology（物理与技术科学中心）
