NPTEL : NOC:Path Integral Methods in Physics and Finance (Management)

Co-ordinators : Prof. J. P. Singh


Lecture 1 - Setting The Scene

Lecture 2 - Introduction to the Path Integral

Lecture 3 - Probability Fundamentals, Generating Functions

Lecture 4 - Generating Functions, Gaussian Distribution

Lecture 5 - Gaussian Distribution, Gaussian Integration

Lecture 6 - Gaussian Integration, Central Limit Theorem

Lecture 7 - Elementary Theory of Stochastic Processes

Lecture 8 - Evolutionary Equations of Stochastic Processes

Lecture 9 - Brownian Motion

Lecture 10 - Diffusion Equation

Lecture 11 - Diffusion Equation Path Integral - 1

Lecture 12 - Diffusion Equation Path Integral - 2, Autocorrelators

Lecture 13 - Schrodinger Equation Path Integral, Langevin Equation

Lecture 14 - Langevin- Equation

Lecture 15 - Statistical Formalism of Path Integral

Lecture 16 - Langevin Equation Path Integral - 1

Lecture 17 - Langevin Equation Path Integral - 2

Lecture 18 - Langevin and Fokker Planck Equation; CLT Example

Lecture 19 - Basic Machinery of Quantum Mechanics

Lecture 20 - Quantum Mechanical Path Integral

Lecture 21 - Harmonic Oscillator Path Integral

Lecture 22 - Free Particle Path Integral

Lecture 23 - Equivalence of Schrodinger and Path Integral Formalisms, Matrix Elements of Operators

Lecture 24 - Ground State Expectation Values

Lecture 25 - Vacuum Persistence Amplitude

Lecture 26 - Harmonic Oscillator 2-Point Problem

Lecture 27 - Relativistic Path Integral

Lecture 28 - Interpretation of Path Integral

Lecture 29 - Need For Quantum Field Theory

Lecture 30 - Quantum Field Theory, Introduction

Lecture 31 - Field Theory Basics

Lecture 32 - Field Theory In Zero Dimensions - 1

Lecture 33 - Field Theory In Zero Dimensions - 2

Lecture 34 - Schwinger Dyson Eqs, Convergence Of Integrals

Lecture 35 - Sde, Feynman Diagrams

Lecture 36 - Feynman Diagrams and Sde

Lecture 37 - Effective Action, Renormalization

Lecture 38 - Renormalization In 0-d

Lecture 39 - Field Theory In 1-D - 1

Lecture 40 - Field Theory in 1-d - 2

Lecture 41 - Euclidean Field Theory - 1

Lecture 42 - Euclidean Field Theory - 2

Lecture 43 - Euclidean Field Theory - 3

Lecture 44 - Field Theory In Minkowski Space

Lecture 45 - Propagator In Minkowski Space

Lecture 46 - Propagator Properties In Minkowski Space

Lecture 47 - Interactive Field Theory In Minkowski Space

Lecture 48 - Causality, Sde In Minkowski Space

Lecture 49 - Sde For Field Theory In Minkowski Space

Lecture 50 - Spinor Fields Path Integral

Lecture 51 - Gauge Fields - 1

Lecture 52 - Gauge Fields - 2

Lecture 53 - Ito Equation, Stock Price Modelling

Lecture 54 - Financial Derivatives

Lecture 55 - Properties Of Options

Lecture 56 - Pricing Of Options: Binomial Model - 1

Lecture 57 - Pricing Of Options: Binomial Model - 2

Lecture 58 - Black Scholes Model

Lecture 59 - Path Integral Solution Of Black Scholes Pde

Lecture 60 - Misc Financial Applications Of Path Integrals