Syllabus
Lecture
1. General description of xAct and some selected examples. Lecture
2. Introduction to the Wolfram Language. Lecture
3. xTensor and its data types: working with tensors and covariant derivatives. Canonicalization of tensorial expressions. Lecture
4. Working with a single and multiple metric tensors. Canonicalization of expressions with a metric tensor. Lecture
5. Canonicalization of expressions with covariant derivatives. Pattern indices. Lecture
6. Implementation of general tensorial rules. Lecture
7. Constant symbols, inert heads, parameters and scalar functions. Lie brackets and vector contraction of tensor slots. Lecture
8. The variational derivative. Working examples with the Einstein-Hilbert action (Palatini formalism), f(R) theory and Lovelock gravity. Lecture
9. The 1+3 decomposition. ADM formalism. Lecture
10. Main differential identities of a Killing vector. The Mars-Simon tensor in vacuum. Lecture
11. The conformal equations. Lecture
12. Component computations with xCoba. Storage of components: the tensor values framework and the CTensor container. Lecture
13. The containers CTensor and CCovD and their converters. The xCoba cache system. Lecture
14. Curvature computations with xCoba. See http://www.xact.es/xActCourse_Prague/ for additional course details. Some practical details about the course (schedule, etc) will be supplied during the meeting with students (Setkání se studenty) on Tuesday 8th October at 10:40. See http://utf.mff.cuni.cz/seminare/semmf.pl
Annotation
It will be explained how tensor analysis can be carried out efficiently within Mathematica/Wolfram Language using xAct system. The applications are mostly tailored for Theoretical Physics and General Relativity but other applications to mechanics of continuous media are also possible.