Lectures related to Antisymmetric tensor

Spherical Tensors and Wigner-Eckart Theorem

Covers the transformation of vectors and tensors in quantum physics.

Explores the transformation of vectors and tensors, including rotations and representations in quantum physics.

Covariant and Contravariant Tensors: Maxwell Field Strength

Explores contravariant and covariant tensors, Maxwell field strength, and Lorentz invariance in linear transformations and metric properties.

Chemical Environments: Representations and Correlations

Explores chemical environment representations, symmetrized correlations, and machine learning applications at the atomic scale.

Vectors and Tensors: Mathematical Preliminaries and Transformations

Explores mathematical preliminaries of tensors and their transformations under basis rotations.

Elements of Lie Groups and Algebras

Explores the transformation of vectors and tensors in quantum physics, emphasizing Lie groups and algebras.

Christoffel Symbols and Gravity Before Einstein

Introduces Christoffel symbols and gravity concepts before Einstein, discussing mathematical tensors and the Nobel Prize in Physics.

Lorentz Covariant Formulation: Maxwell Equations

Covers Lorentz transformations, Maxwell equations, and charge conservation in Lorentz invariant physics.

Mechanical Displacements and Moment Balance

Covers assumptions on small displacements and moment balance in mechanical systems.

Lorentz Transformations and Covariant Tensors

Explores Lorentz transformations, covariant tensors, rotational invariance, and linear transformations in vector spaces.

Scalar, Vector or Tensor? Gravity

Discusses defining tensors, space-time dimensionality, and challenges in formulating a relativistic theory of gravity.

Differential Forms: Basics and Applications

Introduces the concept of differential forms and their applications in n-dimensional manifolds, including the Levi-Civita tensor and volume form.

Covariant Derivatives and Christoffel Symbols

Covers accelerated and inertial coordinate systems, Jacobian, volume elements, covariant derivatives, Christoffel symbols, Lorentz case, and metric tensor properties.

Lorentz Invariance and Covariant Tensors

Explores Lorentz invariance, tensors in vector spaces, and electromagnetic potentials.

Introduction to Continuum Mechanics

Covers scaling, mathematical modeling, tensor notation, and Python exercises in Jupyter notebooks.

Transformation Laws: Diagonalization of Symmetric Tensors

Discusses tensor transformations and diagonalization of symmetric tensors, focusing on stress analysis and the significance of principal stresses.

Special and General Relativity

Introduces special and general relativity, Einstein equations, and gravitational dynamics.

Riemann Tensor and Ricci Scalar

Covers the properties of the Riemann tensor and Ricci scalar in normal coordinates.

Tensors & Indices Recap

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

Representations of SU(2): Symmetries and Transformations

Covers the representations of SU(2) and their transformations in quantum mechanics.