Using Perelman's approach for geometrical flows in terms of an entropy functional, the Higgs mechanism is studied dynamically along flows defined in the space of parameters and in fields space. The model corresponds to two-dimensional gravity that incorporates torsion as the gradient of a Higgs field, and with the reflection symmetry to be spontaneously broken. The results show a discrete mass spectrum, and the existence of a mass gap between the Unbroken Exact Symmetry and the Spontaneously Broken Symmetry scenarios. In the later scenario, the geometries at the degenerate vacua correspond to conformally flat manifolds without torsion; twisted two-dimensional geometries are obtained by building perturbation theory around a ground state; the tunneling quantum probability between vacua is determined along the flows.
The coherent states: old geometrical methods in new quantum clothes
利用相干态流形M-tilda嵌入到射影Hilbert空间中的方法，给出了相干态之间跃迁振幅的一个几何刻画，或者等价地给出了D-M tilda -模中全纯截面的厄米标量积的一个几何刻画.考虑了具有齐次Kaehler结构的相干态流形.利用相干态方法，提出了一种求对称流形和广义对称流形M-tilda上割轨线的有效方法。讨论了旗型相干态流形的CW复结构.本文评述了Anandan和Aharonov关于上世纪射影几何构造的最新结果。用相干态方法进行了有意义的计算，为Y. C. Wong关于复Grassmann流形中共轭轨迹的研究。
On multimatrix models motivated by random noncommutative geometry II: A Yang-Mills-Higgs matrix model
我们继续研究内Connes的频谱形式主义和它们的关系，多矩阵模型的模糊几何。在[arXiv 2007：10914，Ann. Henri Poincaré]的这篇姊妹论文中，我们提出了一个基于非对易几何的规范理论，它--就像几乎对易流形的传统公式一样--也有能力容纳希格斯场。然而，在对比“几乎交换流形”，本框架只采用有限维代数，我们称之为规范矩阵谱三元组。在一个路径积分量子化方法的光谱作用，这允许状态杨米尔斯-希格斯理论（四维欧几里得模糊空间）作为一个显式的随机多矩阵模型在这里获得，其矩阵场镜杨米尔斯-希格斯理论的光滑流形。
