相关论文: Atiyah-Singer Index Theorem in an SO(3) Yang-Mills…
We show that the Atiyah-Singer index theorem of Dirac operator can be directly proved in the canonical formulation of quantum mechanics, without using the path-integral technique. This proof takes advantage of an algebraic isomorphism…
Dirac's quantization condition, $eg=n/2$ ($n \in \Bbb Z$), and Schwinger's quantization condition, $eg=n$ ($n \in \Bbb Z$), for an electric charge $e$ and a magnetic charge $g$ are derived by utilizing the Atiyah-Singer index theorem in two…
If an operator $H$ anticommutes with a chirality operator $\Gamma_*$ such that $\Gamma_*^2=1$, the null space of $H$ can be decomposed in a direct sum of two spaces having positive and negative chiralities, respectively. When both spaces…
We formulate and prove a generalization of the Atiyah-Singer family index theorem in the context of the theory of spaces of manifolds \`a la Madsen, Tillmann, Weiss, Galatius and Randal-Williams. Our results are for Dirac-type operators…
In this talk, we review the heat kernel approach to the Atiyah-Singer index theorem for Dirac operators on closed manifolds, as well as the Atiyah-Patodi-Singer index theorem for Dirac operators on manifolds with boundary. We also discuss…
A new supersymmetric proof of the Atiyah-Singer index theorem is presented. The Peierls bracket quantization scheme is used to quantize the supersymmetric classical system corresponding to the index problem for the twisted Dirac operator.…
We formulate and prove a lattice version of the Atiyah-Singer index theorem. The main theorem gives a $K$-theoretic formula for an index-type invariant of operators on lattice approximations of closed integral affine manifolds. We apply the…
The Atiyah-Singer index theorem is a topological formula for the index of an elliptic differential operator. The topological index depends on a cohomology class that is constructed from the principal symbol of the operator. On contact…
The Atiyah-Singer index theorem, a cornerstone of modern mathematics, has traditionally been derived from supersymmetric (SUSY) physics. This paper demonstrates a direct derivation from non-supersymmetric quantum statistics by establishing…
The Atiyah-Singer index theorem, a landmark achievement of the early 1960s, brings together ideas in analysis, geometry, and topology. We recount some antecedents and motivations; various forms of the theorem; and some of its implications,…
The index theorem, discovered by Atiyah and Singer in 1963, is one of most important results in the twentieth century mathematics. It found numerous applications in analysis, geometry and physics. Since it was discovered numerous attempts…
Let M be a compact manifold with a fixed spin structure \chi. The Atiyah-Singer index theorem implies that for any metric g on M the dimension of the kernel of the Dirac operator is bounded from below by a topological quantity depending…
K-theory allows us to define an analytical condition for the existence of `false' gauge field copies through the use of the Atiyah-Singer index theorem. After establishing that result we discuss a possible extension of the same result…
The quantization of the superclassical system used in the proof of the index theorem results in a factor of $\hbar^{2}R/8 $ in the Hamiltonian. The path integral expression of the kernel is analyzed up to and including 2-loop order. The…
We consider the index of a Dirac operator on a compact even dimensional manifold with a domain wall. The latter is defined as a co-dimension one submanifold where the connection jumps. We formulate and prove an analog of the…
We prove an Atiyah-Patodi-Singer index theorem for Dirac operators twisted by C*-vector bundles. We use it to derive a general product formula for eta-forms and to define and study new rho-invariants generalizing Lott's higher rho-form. The…
We give a cohomological formula for the index of a fully elliptic pseudodifferential operator on a manifold with boundary. As in the classic case of Atiyah-Singer, we use an embedding into an euclidean space to express the index as the…
The purpose of this work is to give a new and short proof of Atiyah-Singer local index theorem by using heat semigroups approximations based on the truncature of Brownian Chen series.
We discuss the interplay between topologically non-trivial gauge field configurations and the spectrum of the Wilson-Dirac operator in lattice gauge theory. Our analysis is based on analytic arguments and numerical results from a lattice…
We give a very simple derivation of the Atiyah-Patodi-Singer (APS) index theorem and its small generalization by using the path integral of massless Dirac fermions. It is based on the Fujikawa's argument for the relation between the axial…