AI 中文总结
研究具有非平凡 CF 型限制的 D 维自由阿贝尔 2 - 形式规范理论的 BRST 量子化版本，利用高斯散度定理和正则对易子证明诺特定理（反）BRST 荷幂零性质，推导修正荷并证明其不变性，讨论物理性标准及后者相对于前者的优越性。
AI 中文摘要
在贝奇 - 鲁埃 - 斯托拉 - 秋京（BRST）形式体系框架内，我们利用基本正则（反）对易子的性质，证明了具有非平凡库尔奇 - 费拉里（CF）型限制的 D 维自由阿贝尔 2 - 形式规范理论的 BRST 量子化版本中诺特定理（反）BRST 荷的幂零性质。证明仅使用高斯散度定理。在壳外幂零（反）BRST 对称变换下，诺特定理守恒（反）BRST 荷不不变且非壳外幂零。但若在合适位置使用适当运动方程及高斯散度定理，这些荷会变为（反）BRST 不变且幂零。我们推导了在壳外幂零（反）BRST 变换下不变的诺特定理（反）BRST 荷的一致修正版本，并利用基本正则（反）对易子证明了这些修正荷的（反）BRST 不变性。我们还讨论了关于守恒诺特定理（反）BRST 荷以及修正后的（反）BRST 不变版本的诺特定理（反）BRST 荷的物理性标准，证明了后者相对于前者的优越性（从与规范理论的狄拉克量子化条件的一致性来看）。
英文摘要
Within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism, we invoke the beauty of the basic canonical (anti)commutators to prove the nilpotency property of the Noether (anti-)BRST charges for the D-dimensional BRST-quantized version of the free Abelian 2-form gauge theory which is endowed with a non-trivial Curci-Ferrari (CF) type restriction. In this proof, we use only the theoretical strength of the Gauss divergence theorem. We demonstrate that, under the off-shell nilpotent (anti-)BRST symmetry transformations, the Noether conserved (anti-)BRST charges are not invariant and they are also found to be not off-shell nilpotent (if we exploit the standard relationship between the continuous symmetry transformations and their generators as the Noether conserved charges). However, these charges become (anti-)BRST invariant and nilpotent if we use (i) the appropriate equations of motion at suitable places, and (ii) the Gauss divergence theorem. We derive the consistently modified versions of the Noether (anti-)BRST charges which are invariant under the off-shell nilpotent (anti-)BRST transformations. We prove the (anti-)BRST invariance of these modified versions of charges by using the basic canonical (anti)commutators, too. We discuss the physicality criteria w.r.t. (i) the conserved Noether (anti-)BRST charges, and (ii) the modified (anti-)BRST invariant versions of the Noether (anti-)BRST charges. We prove the superiority of the latter over the former (in view of the consistency with the Dirac quantization conditions for the gauge theories).
CommentsLaTeX file, 37 pages v2: typos fixed, a new footnote added, minor modifications in the text
