디랙 연산자

노트

위키데이터

• ID : Q907439

말뭉치

1. Another Dirac operator arises in Clifford analysis.
2. Here we visualize eigenfunctions of Laplace-Beltrami (left) which ignores extrinsic bending, and our relative Dirac operator (right) which ignores intrinsic stretching.
3. We introduce a new extrinsic differential operator called the relative Dirac operator, leading to a family of operators with a continuous trade-off between intrinsic and extrinsic features.
4. A general eigenvalue problem for the Dirac operator on a metric manifold M in terms of spinor and tangent fields defined via the Clifford algebra is derived herein.
5. Eigenvalues and eigenfunctions for the Dirac operator on any sphere or pseudosphere are determined.
6. In this section we collect general facts on the \(L^p\)-spectrum of the Dirac operator.
7. We derive upper eigenvalue bounds for the Dirac operator of a closed hypersurface in a manifold with Killing spinors such as Euclidean space, spheres or hyperbolic space.
8. In higher codimension we obtain bounds on the eigenvalues of the Dirac operator of the submanifold twisted with the spinor bundle of the normal bundle.
9. These lectures aim to give an elementary exposition on basic results about the first eigenvalue of the Dirac operator, on compact Riemannian Spin manifolds with positive scalar curvature.
10. We end by pointing out how the size of the gap around zero in the spectrum of the Dirac operator, increases when the geometrical structure is Kähler or Quaternion-Kähler.
11. Applications of this result include the construction of non-isotopic metrics with invertible Dirac operator, and a concordance existence and classification theorem.
12. Note that as \(r\longrightarrow +\infty\), the Dirac operator becomes \(-i\sigma_1 e_1 - i\sigma_2 e_2\), which is the spin-Dirac operator on \(\mathbb{R}^2\).
13. The spectrum The spin-Dirac operator is a first order, self-adjoint elliptic operator, which implies (as \(S^2\) is compact) that it has a discrete spectrum.
14. I really like Thomas Friedrich's Dirac Operators in Riemannian Geometry, I think it's a great reference for this stuff.
15. It should be obvious why the Dirac operator is important in physics because of fermions.