规范群

We prove that on the localgauge group C∞(M a compact manifold,G a matrix Lie group)there does not exist afinite translationally invariant Borel measure.

我们证明了在局域规范群C∽(M为一紧致流形，G为一矩阵李群)上不存在有限的平移不变的Borel测度。

Here the key assumption is the existence of a translationallyinvariant measure on the local gauge group.

这里一个关键的假设是局域规范群上存在一个平移不变的测度。

The Standard Model of elementary particles is a theory based on the gauge group of SU(3)_C ?

标准模型是建立在规范群SU(3)_C ？

The local gauge group is infinite dimensional and not lo-cally compact,hence the existence of an invariant measure deserves careful study.

局域规范群是无限维和非局部紧致的，因此其上不变测度的存在性值得仔细研究。

Besides the above main work of this thesis,we also do some other work related to the electroweak chiral Lagrangian,for instance we calculate the contributions to the oblique correction parameters S,T and U from heavy fermions and scalars in some generic representations of the electroweak gauge group.

除上述这些本论文工作的主要部分之外，我们还做了一些与电弱手征拉氏量相关的其它工作，例如我们计算了处于电弱规范群的一些一般表示的重费米子和重标量场对oblique修正参数S，T和U的贡献。

In noncommutative scalar field theories, the appearing of nonplanar diagrams is related to permutation symmetry of field functions in the interaction Lagrangian, while in NCQED we can not arbitrarily change the positions of field functions in the interaction Lagrangian because different positions of the field functions correspond to different representations of the gauge group.

这里需要特别指出的是NCQED的非平面图产生的原因与非对易标量场根本不同，非对易标量场非平面图的产生是和相互作用拉氏量密度中场函数间位置的置换对称性有关，而在NCQED中我们不能随便交换相互作用拉氏量密度中场函数的位置，因为场函数的不同位置对应着规范群的不同表示。

After descibing the concepts, definitionsand operation approaches of quantum group and SLq(2) Lie algebra, the physicalmeaning of quantum group particles is explained in the present thesis. The gaugeinvariance in SLq(2) gauge field and its thermodynamics model is considered basedon the idea of q-deformation. The zero energy gap equation and q-deformed energygap equation are derived under the assumption of q-quantization and semi-classical q-quantization, then the zero-temperature energy gap A(0,q) and crititical temperature〓 can be calculated from the q-energy gap equation.

在介绍了量子群和SLq(2)李代数的基本概念，定义和运算方法后，文中进一步阐述了量子群粒子的物理意义；在q变形思想基础上，本文研究了SLq(2)规范场及其热力学模型中的规范不变性质，并在q量子化和半经典q量子化的假设下导出了零能隙方程和q变形能隙方程；然后从q能隙方程计算了与零温度能隙△(0，q)和临界温度〓。

In this paper we will mainly study the gauge fixing Yang-Mills heat flow of a principal bundle For a principle bundle with a compact seme-simple Lie group as its structure group over a compact Riemannian manifold without boundary, the evolutions of the curvature and its higher derivatives under the flow above will be derived, and the energy inequality and the Bochner type estimates will be obtained.

中文摘要：本论文主要讨论主丛上的规范固定Yang-Mills热流我们在紧致无边黎曼流形上的以半单紧致李群为结构群的主丛上，推导了在规范固定Yang-Mills热流下曲率及其高阶导数的演化方程，得到了该热流的能量不等式和Bochner估计，由此可推出单调性公式和小作用量正则性，以及曲率各阶导数的局部一致估计。

In this paper we will mainly study the gauge fixing Yang-Mills heat flow of a principal bundleFor a principle bundle with a compact seme-simple Lie group as its structure group over a compact Riemannian manifold without boundary, the evolutions of the curvature and its higher derivatives under the flow above will be derived, and the energy inequality and the Bochner type estimates will be obtained. Then, the monotonicity formula and the small action regularity theorem can be proved. We will give the locally uniform estimates for the higher derivatives of the curvature.

本论文主要讨论主丛上的规范固定Yang-Mills热流我们在紧致无边黎曼流形上的以半单紧致李群为结构群的主丛上，推导了在规范固定Yang-Mills热流下曲率及其高阶导数的演化方程，得到了该热流的能量不等式和Bochner估计，由此可推出单调性公式和小作用量正则性，以及曲率各阶导数的局部一致估计。

The second part deals with renormalization group equations in general gauge field theories. In this part, the complete set of two-loop renormalization group equations in general gauge field theories is presented.

第二个部分主要讲述了规范场理论中的两圈重整化群方程，我们给出了一组完整的一般规范场的两圈重整化群方程。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。