Tensor Analysis

Major
Physics
Quarter
Spring
Year
2021
Course Number
Physics CS 140TA, Section 1
Enrollment Code
64246
Instructor(s)
Date & Time
TR 11:00AM- 12:15PM (Synchronous)
Location
On Line

Course Description

Special Relativity. Flat spacetime.

1. Lorentz transformations. Basis vectors.
2. The Lorenz group.
3. Scalars, vectors and tensors in flat spacetime. Coordinate free notation.
4. Operations with tensors.
5. Electromagnetic potentials. Coulomb gauge and Lorentz gauge.
6. The electromagnetic field tensor.
7. Maxwell’s equations in covariant form.
8. Transformations of electromagnetic fields.

General relativity. Curved spacetime:

9. Curvilinear coordinates. Scalars, vectors and tensors in curved spacetime. Tensors as geometric objects.
10. Parallel transport. Geodesics. Motion in gravitational fields.
11. Covariant derivatives.
12. The Riemann curvature tensor.
13. The Ricci tensor. Einstein’s equations.
14. The Schwartzschild metric.

Required Text

Bernard F. Schutz “A First Course in General Relativity” Cambridge University Press
P.A.M. Dirac, “General Theory of Relativity” Princeton University Press