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