Spectral asymmetry of the massless Dirac operator on a 3 - torus
نویسندگان
چکیده
منابع مشابه
Spectral analysis of the massless Dirac operator on a 3-manifold
The talk will give an overview of our further development of the paper [7] by Robert Downes, Michael Levitin and Dmitri Vassiliev and it will also give an insight how spectrum of massless Dirac operator on a 3-manifold interplays with geometric contents of the manifold. In contrast to the Riemann flat manifold studied in [7], 3-torus, we study the massless Dirac operator on a 3-sphere equipped ...
متن کاملInverse Problem for Interior Spectral Data of the Dirac Operator with Discontinuous Conditions
In this paper, we study the inverse problem for Dirac differential operators with discontinuity conditions in a compact interval. It is shown that the potential functions can be uniquely determined by the value of the potential on some interval and parts of two sets of eigenvalues. Also, it is shown that the potential function can be uniquely determined by a part of a set of values of eigenfun...
متن کاملDirac Operator and Eigenvalues in Riemannian Geometry PROGRAM
Lecture 2. Index problem for manifolds with a boundary. Index of the Dirac operator and anomalies. Lecture 3. Spectral asymmetry and Riemannian geometry. Heat equation and asymptotic heat kernel. The η-and ζ-functions. Lecture 4. Two-component spinor calculus. Dirac and Weyl equations in two-component spinor form. Weyl equation with spectral or local boundary conditions. Potentials for massless...
متن کاملFinite gap theory of the Clifford torus
In this paper we construct the spectral curve and the Baker–Akhiezer function for the Dirac operator which form the data of the Weierstrass representation of the Clifford torus. This torus appears in many conjectures from differential geometry (see Section 2). By constructing this Baker–Akhiezer function we demonstrate a general procedure for constructing Dirac operators and their Baker–Akhieze...
متن کاملSpectral theoretic characterization of the massless Dirac operator
We consider an elliptic self-adjoint first-order differential operator acting on pairs (2-columns) of complex-valued half-densities over a connected compact three-dimensional manifold without boundary. The principal symbol of our operator is assumed to be trace-free. We study the spectral function which is the sum of squares of Euclidean norms of eigenfunctions evaluated at a given point of the...
متن کامل