xAct Lectures

Lecture notebooks on xAct, the Wolfram Language suite for tensor computer algebra. Source: xact.es

These lecture notes are based on the notebooks developed by Alfonso García-Parrado during his stay at Institute of Theoretical Physics, Prague in 2018.

Lectures, Thursdays 16:30, ÚTF, ZS26/27

1. General description of xAct and some selected examples
2. Introduction to the Wolfram Language
3. xTensor and its data types: working with tensors and covariant derivatives. Canonicalization of tensorial expressions
4. Working with a single and multiple metric tensors. Canonicalization of expressions with a metric tensor
5. Canonicalization of expressions with covariant derivatives. Pattern indices
6. Implementation of general tensorial rules
7. Constant symbols, inert heads, parameters and scalar functions. Lie brackets and vector contraction of tensor slots
8. The variational derivative. Working examples with the Einstein–Hilbert action (Palatini formalism), f(R) theory and Lovelock gravity
9. The 1+3 decomposition: ADM formalism
10. Main differential identities of a Killing vector. The Mars–Simon tensor in vacuum
11. The conformal equations
12. Component computations with xCoba. Storage of components: the tensor values framework and the CTensor container
13. The containers CTensor and CCovD and their converters. The xCoba cache system
14. Curvature computations with xCoba

Other files

• Lectures.nb
• PublicNPGHP.nb