Lectures related to Symmetry in Integrals & Matrix Elements

Eigenstate Thermalization Hypothesis

Explores the Eigenstate Thermalization Hypothesis in quantum systems, emphasizing the random matrix theory and the behavior of observables in thermal equilibrium.

Taylor Series and Definite Integrals

Explores Taylor series for function approximation and properties of definite integrals, including linearity and symmetry.

Discrete Symmetries: Asymptotic States and S-matrix

Covers the concept of discrete symmetries, focusing on the introduction to asymptotic states and S-matrix.

Symmetry in Integrals

Explores how symmetries can simplify integrals with interesting cases and examples.

Examples of Integrals

Explores calculating areas under different functions, showcasing the concept of reciprocal functions and symmetry.

Symmetry & Group Theory

Covers the fundamental concepts of symmetry and group theory.

Inertia Tensor: Main Axes and Principal Moments

Explains the inertia tensor, main axes, principal moments, and balancing of rotating solids.

Quantum Mechanics: Operators and Eigenvalues

Covers matrix elements, operators, paths with conditions, and time evolution in quantum mechanics.

Symmetry in XCOSV-y-Sind

Explores symmetry in XCOSV-y-Sind and staggered ethane molecules.

Linear Algebra: Matrices and Linear Applications

Covers matrices, linear applications, vector spaces, and bijective functions.

Improper Integrals: Convergence and Comparison

Explores improper integrals, convergence criteria, comparison theorems, and solid revolution.

Determinant, Area, and Volume

Explores area determination, linear applications, matrix operations, and vector spaces.

Electric Potential and Gauss's Law

Explores electric potential, the principle of superposition, and Gauss's law.

Analytic Continuation: Residue Theorem

Covers the concept of analytic continuation and the application of the Residue Theorem to solve for functions.

Functions xr, r>0, on 10,1

Covers the properties of functions xr, r>0, on 10,1, including limits and integrals.

Conformal Field Theory & Operator Product Expansion

Explores Conformal Field Theory and Operator Product Expansion, emphasizing the role of symmetries and the quantization process in CFT.

Advanced Analysis II: Sequences and Integrals

Explores sequences, integrals, symmetrical functions, differential equations, and the Cauchy problem in advanced analysis.

Asymptotic States and S-matrix

Covers the concept of asymptotic states and S-matrix in quantum field theory, focusing on the evolution of wave packets and the scattering states.

Two-loop Computations: External Legs and Internal Propagators

Covers the computation of two-loop diagrams with external legs and internal propagators.

Orthogonal Projections: Symmetry and Matrices

Explores orthogonal projections, symmetry of matrices, and their applications.