Spinor Analysis on Riemannian 3-manifolds | |
Student No.： | 50 |
Time： | Tue/Thu15:30-17:00, 2013-02-25~ 2013-06-05(except for public holidays) |
Instructor： | Abul Masood-ul-Alam [Tsinghua University] |
Place： | Conference Room 3, Floor 2, Jin Chun Yuan West Building |
Starting Date： | 2014-2-25 |
Ending Date： | 2014-6-5 |
Description:
Spinors have important applications in general relativity and differential geometry. Unlike the case of tensor analysis much of spinoranalysis is masked by representation theory jargons, which vary considerably with dimension and metric signature, thus becoming difficult and time consuming for analysts. Although tensors are also elements of representation spaces, and we decompose tensors belonging to invariant subspaces, with tensors we do much computation without going deep into representation theory. Aim of this course is to learn performing similar applications with spinors. We start with SU(2) spinors in 3-dimension from very basics, learn to do calculation in local coordinates, study Dirac equation and positive mass theorem. Finally we study SL(2,C) spinors in 3+1 space-times. The course is suitable for both graduate and senior level undergraduate students.
Prerequisite:
Geometry: manifolds, knowledge of Christoffel symbols and curvature, or concurrent enrollment in a Riemannian Geometry course.
Reference:
8. “Eigenvalue Boundary Problems for the Dirac Operator,” O. Hijazi, S. Montiel, A. Roldan, Commun. Math. Phys. 231 (2002) 375-390.
Multivariable Calculus, Real Analysis and Linear Algebra.