Lectures related to Killing vector field

Covers the quantization of topological operators and Ising models on square lattices.

Exponential Maps: Properties and Applications in Lie Groups

Covers the properties of the exponential map in Lie groups and their algebras, including smoothness and the relationship between subgroups and algebras.

Tensor Transformations

Introduces tensor transformations, rotation matrices, and differential operators in mechanics.

Vector Fields and Lorentz Tensors: Representation Theory

Covers the transformation properties of vector fields and their representation in Lorentz tensors.

Properties of the Exponential Map

Explores the properties of the exponential map in Lie groups and algebras.

Tensors & Indices Recap

Covers the basics of tensors and indices, including contravariant vectors and tensor operations.

Linear Lie Groups: Definitions and Theorems

Discusses linear Lie groups, their definitions, properties, and the relationship between integral curves and vector fields.