Symmetry and Topology of Matter and Gravitational Fields

(1)导出了三维非线性σ模型的Wilson重整化群方程。共形不变场论被定义为该方程的不动点理论。Einstein-Kahler流形上的非线性sigma模型对应于紫外不动点。(2)规范场和希格斯场在高维引力理论的框架下得到了统一。标准电弱理论中的希格斯场与额外维度中的Aharanov-Bohm相一致。现实的模型上构建的五维扭曲时空。(3)计算了中微子反应散射截面的辐射修正。特别注意G_A/G_V比值的辐射校正。(4)找到了完整量子计算的精确解。

(1) The Wilsonian renormalization group equation for three dimensional nonlinear sigma models was derived. Conformal invariant field theories are defined as the fixed point theory of that equation. Nonlinear sigma models on Einstein-Kahler manifolds correspond to ultraviolet fixed points. (2) Gauge and Higgs fields are unified in the framework of higher dimensional gravity theory. Higgs fields in the standard electroweak theory are identified with the Aharanov-Bohm phase in the extra-dimensions. Realistic models are constructed on the five-dimensional warped spacetime. (3) Radiative corrections were calculated for the scattering cross sections in neutrino reactions. Special care was exercised for the radiative correction in G_A/G_V ratio. (4) Exact solutions of holonomic quantum computation are found.