Lectures related to Nonadiabatic Dynamics: Quantum-Classical Methods

Curve Integrals of Vector Fields

Explores curve integrals of vector fields, energy calculations, potential functions, and tangential vectors, with a focus on line integrals and domains.

Complex Analysis: Derivatives and Integrals

Provides an overview of complex analysis, focusing on derivatives, integrals, and the Cauchy theorem.

Curve Integrals: Gauss/Green Theorem

Explores the application of the Gauss/Green theorem to calculate curve integrals along simple closed curves.

Green's Theorem: Applications

Covers the application of Green's Theorem in analyzing vector fields and calculating line integrals.

Integration Techniques: Change of Variable and Integration by Parts

Explores advanced integration techniques such as change of variable and integration by parts to simplify complex integrals and solve challenging integration problems.

Gauge Theories: Chiral Transformations and Path Integrals

Covers the gauged Wess-Zumino-Witten model and its applications in conformal field theory.

Green's Theorem: Understanding Rotations and Closed Paths

Explores Green's Theorem, rotations, closed paths, and integral signs.

Small Instantons and Axion Mass

Explores small instantons, axion mass, Strong CP problem, and extra dimensions.

Integration of Path: Part 2

Covers the continuation of path integrals, focusing on complex functions and their applications.

Residue Theorem: Applications in Complex Analysis

Discusses the residue theorem and its applications in complex analysis, including integral calculations and Laurent series.

Complex Analysis: Cauchy Integral Formula

Explores the Cauchy integral formula in complex analysis and its applications in evaluating complex integrals.

Green's Theorem: Boundary and Normal Vectors

Explores boundaries, normal vectors, and Green's theorem application in transforming integrals.

Integrals of Paths

Covers the concept of integrals of paths with examples and applications.

Green's Theorem: Transforming Integrals in 2D

Covers Green's Theorem, transforming 2D integrals into 1D line integrals.

Complex Integration and Cauchy's Theorem

Discusses complex integration and Cauchy's theorem, focusing on integrals along curves in the complex plane.

Curl of Vector Field and Path Integrals

Explores the curl of a vector field and the calculation of path integrals in Cartesian coordinates.

Vector Calculus: Green's Theorem

Explores Green's theorem, vector field curl, Ampère's law, and magnetic field modeling.

Quantum Field Theory: Path Integrals

Explores path integrals in quantum field theory, emphasizing the significance of Wick rotation and the classical case.

Constructing Correlators with Path Integrals

Explores constructing correlators using path integrals in quantum mechanics, focusing on the Euclidean and Minkowski spaces and the significance of imaginary time evolution.

Electric Fields: Curl and Path Integrals, Spherical Coordinates Supplement

Explores the integration of electric fields along paths and solutions for constant and radial fields.