In this paper we show that the de Rham and the Signature operators on a Riemannian manifold are all isomorphic to some twisted Atiyah-Singer operators. Then the local index theorem and local Lefschetz fixed point form...In this paper we show that the de Rham and the Signature operators on a Riemannian manifold are all isomorphic to some twisted Atiyah-Singer operators. Then the local index theorem and local Lefschetz fixed point formulas of these operators can be obtained from the corresponding theorems of twisted Atiyah-Singer operators.展开更多
It is shown that a novel anomaly associated with transverse Waxd-Takahashi identity exists for a pseudo- tensor current in QED, and the anomaly gives rise to a topological index of a Dirac operator in terms of an Atiy...It is shown that a novel anomaly associated with transverse Waxd-Takahashi identity exists for a pseudo- tensor current in QED, and the anomaly gives rise to a topological index of a Dirac operator in terms of an Atiyah- Singer index theorem.展开更多
A topological way to distinguish divergences of the Abelian axial-vector current in quantum field theory is proposed. By using the properties of the Atiyah-Singer index theorem, the nomtrivial Jacobian factor of the i...A topological way to distinguish divergences of the Abelian axial-vector current in quantum field theory is proposed. By using the properties of the Atiyah-Singer index theorem, the nomtrivial Jacobian factor of the integration measure in the path-integral formulation of the theory is connected with the topological properties of the gauge field. The singularity of the fermion current related to the topological character can be correctly examined in a gauge background.展开更多
挪威科学与艺术学院决定把2004年度的Abel奖颁发予Edinburgh大学的Michael Francis Atiyah爵士和MIT(麻省理工学院)的Isadore M．Singer，以表彰“他们运用拓扑、几何和分析，发现并证明了指标定理，以及他们在数学与理论物理之间构建...挪威科学与艺术学院决定把2004年度的Abel奖颁发予Edinburgh大学的Michael Francis Atiyah爵士和MIT(麻省理工学院)的Isadore M．Singer，以表彰“他们运用拓扑、几何和分析，发现并证明了指标定理，以及他们在数学与理论物理之间构建新桥梁中的杰出作用．”展开更多
The purpose of this paper is to give a refinement of the Atiyah-Singer families index theorem at the level of differential characters. Also a Riemann-Roch-Grothendieck theorem for the direct image of flat vector bundl...The purpose of this paper is to give a refinement of the Atiyah-Singer families index theorem at the level of differential characters. Also a Riemann-Roch-Grothendieck theorem for the direct image of flat vector bundles by proper submersions is proved,with Chern classes with coefficients in C/Q. These results are much related to prior work of Gillet-Soule, Bismut-Lott and Lott.展开更多
文摘In this paper we show that the de Rham and the Signature operators on a Riemannian manifold are all isomorphic to some twisted Atiyah-Singer operators. Then the local index theorem and local Lefschetz fixed point formulas of these operators can be obtained from the corresponding theorems of twisted Atiyah-Singer operators.
基金Supported by National Natural Science Foundation of China(10775059)
文摘It is shown that a novel anomaly associated with transverse Waxd-Takahashi identity exists for a pseudo- tensor current in QED, and the anomaly gives rise to a topological index of a Dirac operator in terms of an Atiyah- Singer index theorem.
文摘A topological way to distinguish divergences of the Abelian axial-vector current in quantum field theory is proposed. By using the properties of the Atiyah-Singer index theorem, the nomtrivial Jacobian factor of the integration measure in the path-integral formulation of the theory is connected with the topological properties of the gauge field. The singularity of the fermion current related to the topological character can be correctly examined in a gauge background.
文摘The purpose of this paper is to give a refinement of the Atiyah-Singer families index theorem at the level of differential characters. Also a Riemann-Roch-Grothendieck theorem for the direct image of flat vector bundles by proper submersions is proved,with Chern classes with coefficients in C/Q. These results are much related to prior work of Gillet-Soule, Bismut-Lott and Lott.
