# Path Integral Methods in Physics & Finance

- Institution: IIT Roorkee
- Department: Management
- Teacher: Prof. J. P. Singh
- Level: Undergraduate
- Language: English
- Subjects: Business and management
- Source: [NPTEL](https://nptel.ac.in/courses/110107146)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/110107146)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

With the gradual acceptance of “path integral” based “string theory” as a strong candidate for unification, knowledge of the nuances of the “path integral” formalism of QFT is indispensable for academic progression in this area. The applications of this versatile concept are also growing by the day, one of the cardinal ones being in pricing of complex financial assets. Scientific risk management by the investor fraternity has become of cardinal necessity for generating competitive returns and surviving in the marketplace. Derivatives have proven to be immensely useful in the management of financial risk. Their vitality can be gauged from the exponential growth in trading volumes as well as the advent of new structured products literally on a day to day basis. Derivatives in petroleum and natural gas industries in the United States are, now, well entrenched, and they are being extensively used in the electricity industry as well. This has called for advent of innovative methods for the pricing of such instruments. With enhanced computing power being accessible, the “path integral formalism” is gradually becoming the method of choice in this context.

INTENDED AUDIENCE : The audience would comprise of those desirous of getting acquainted with the intricacies of the path integral formalism and its applications in contemporary physics, (quantum field theory, in particular) and finance (pricing of path dependent and exotic options and other derivatives) and also, appreciating the nuances that have led to the origin and extensive development of this field of knowledge. PREREQUISITES : (i) Basics of classical & quantum mechanics; (ii) Basics of financial derivatives; (iii) Senior school mathematics (algebra, calculus & probability).

## Lectures

1. [Setting The Scene](https://invisiblenetwork.ai/learn/nptel/110107146/0dc9430a7f9e) (YouTube)
2. [Introduction to the Path Integral](https://invisiblenetwork.ai/learn/nptel/110107146/bc5e613826b3) (YouTube)
3. [Probability Fundamentals, Generating Functions](https://invisiblenetwork.ai/learn/nptel/110107146/080fa57f08ad) (YouTube)
4. [Generating Functions, Gaussian Distribution](https://invisiblenetwork.ai/learn/nptel/110107146/608808d91520) (YouTube)
5. [Gaussian Distribution, Gaussian Integration](https://invisiblenetwork.ai/learn/nptel/110107146/2e5d59fe5127) (YouTube)
6. [Gaussian Integration, Central Limit Theorem](https://invisiblenetwork.ai/learn/nptel/110107146/eb90de98025a) (YouTube)
7. [Elementary Theory of Stochastic Processes](https://invisiblenetwork.ai/learn/nptel/110107146/b2d007ba8922) (YouTube)
8. [Evolutionary Equations of Stochastic Processes](https://invisiblenetwork.ai/learn/nptel/110107146/a569760e986d) (YouTube)
9. [Brownian Motion](https://invisiblenetwork.ai/learn/nptel/110107146/a51a1d0bedaa) (YouTube)
10. [Diffusion Equation](https://invisiblenetwork.ai/learn/nptel/110107146/a4288ae1d27c) (YouTube)
11. [Diffusion Equation Path Integral (1)](https://invisiblenetwork.ai/learn/nptel/110107146/aa96c8cbb44d) (YouTube)
12. [Diffusion Equation Path Integral (2), Autocorrelators](https://invisiblenetwork.ai/learn/nptel/110107146/92a12b6d69fd) (YouTube)
13. [Schrodinger Equation Path Integral, Langevin Equation](https://invisiblenetwork.ai/learn/nptel/110107146/3b1daf3eee1f) (YouTube)
14. [Langevin Equation](https://invisiblenetwork.ai/learn/nptel/110107146/a216d46bad56) (YouTube)
15. [Statistical Formalism of Path Integral](https://invisiblenetwork.ai/learn/nptel/110107146/41de9501ac2a) (YouTube)
16. [Langevin Equation Path Integral (1)](https://invisiblenetwork.ai/learn/nptel/110107146/6102ae74e206) (YouTube)
17. [Langevin Equation Path Integral (2)](https://invisiblenetwork.ai/learn/nptel/110107146/026e7ea6c1f2) (YouTube)
18. [Langevin & Fokker Planck Equation; CLT Example](https://invisiblenetwork.ai/learn/nptel/110107146/c3e42227f062) (YouTube)
19. [Basic Machinery of Quantum Mechanics](https://invisiblenetwork.ai/learn/nptel/110107146/8faef95c8dd5) (YouTube)
20. [Quantum Mechanical Path Integral](https://invisiblenetwork.ai/learn/nptel/110107146/7a286786b07a) (YouTube)
21. [Harmonic Oscillator Path Integral](https://invisiblenetwork.ai/learn/nptel/110107146/5d8823d1fff2) (YouTube)
22. [Free Particle Path Integral](https://invisiblenetwork.ai/learn/nptel/110107146/7d3cd4792f9a) (YouTube)
23. [Equivalence of Schrodinger & Path Integral Formalisms, Matrix Elements of Operators](https://invisiblenetwork.ai/learn/nptel/110107146/f502d4e6ddf7) (YouTube)
24. [Ground State Expectation Values](https://invisiblenetwork.ai/learn/nptel/110107146/d00379c99cf2) (YouTube)
25. [Vacuum Persistence Amplitude](https://invisiblenetwork.ai/learn/nptel/110107146/c49edc91a23f) (YouTube)
26. [Harmonic Oscillator 2-Point Problem](https://invisiblenetwork.ai/learn/nptel/110107146/f81c2efe8530) (YouTube)
27. [Relativistic Path Integral](https://invisiblenetwork.ai/learn/nptel/110107146/bc4fdf8d0c12) (YouTube)
28. [Interpretation of Path Integral](https://invisiblenetwork.ai/learn/nptel/110107146/c8c4dee63ac3) (YouTube)
29. [Need For Quantum Field Theory](https://invisiblenetwork.ai/learn/nptel/110107146/9d44649b961c) (YouTube)
30. [Quantum Field Theory, Introduction](https://invisiblenetwork.ai/learn/nptel/110107146/faf58785f181) (YouTube)
31. [Field Theory Basics](https://invisiblenetwork.ai/learn/nptel/110107146/118668bc13e6) (YouTube)
32. [Field Theory In Zero Dimensions (1)](https://invisiblenetwork.ai/learn/nptel/110107146/b537db1a5f48) (YouTube)
33. [Field Theory In Zero Dimensions (2)](https://invisiblenetwork.ai/learn/nptel/110107146/0e8f9fac7a96) (YouTube)
34. [Schwinger Dyson Eqs, Convergence Of Integrals](https://invisiblenetwork.ai/learn/nptel/110107146/21f23653117a) (YouTube)
35. [Sde, Feynman Diagrams](https://invisiblenetwork.ai/learn/nptel/110107146/3bb58a046e34) (YouTube)
36. [Feynman Diagrams & Sde](https://invisiblenetwork.ai/learn/nptel/110107146/90f306b2c39e) (YouTube)
37. [Effective Action, Renormalization](https://invisiblenetwork.ai/learn/nptel/110107146/316202d0ce6b) (YouTube)
38. [Renormalization In 0-d](https://invisiblenetwork.ai/learn/nptel/110107146/56709b9c8554) (YouTube)
39. [Field Theory In 1-D (1)](https://invisiblenetwork.ai/learn/nptel/110107146/afb8f81cbb03) (YouTube)
40. [Field Theory in 1-d (2)](https://invisiblenetwork.ai/learn/nptel/110107146/8b8c4e4f760e) (YouTube)
41. [Euclidean Field Theory (1)](https://invisiblenetwork.ai/learn/nptel/110107146/63d1c07794cc) (YouTube)
42. [Euclidean Field Theory (2)](https://invisiblenetwork.ai/learn/nptel/110107146/9d762a80432a) (YouTube)
43. [Euclidean Field Theory (3)](https://invisiblenetwork.ai/learn/nptel/110107146/efd103f371a8) (YouTube)
44. [Field Theory In Minkowski Space](https://invisiblenetwork.ai/learn/nptel/110107146/d0c06018a4f9) (YouTube)
45. [Propagator In Minkowski Space](https://invisiblenetwork.ai/learn/nptel/110107146/4909e521365b) (YouTube)
46. [Propagator Properties In Minkowski Space](https://invisiblenetwork.ai/learn/nptel/110107146/984ce3093a8d) (YouTube)
47. [Interactive Field Theory In Minkowski Space](https://invisiblenetwork.ai/learn/nptel/110107146/6ea4267b2c8f) (YouTube)
48. [Causality, Sde In Minkowski Space](https://invisiblenetwork.ai/learn/nptel/110107146/1fe30beae648) (YouTube)
49. [Sde For Field Theory In Minkowski Space](https://invisiblenetwork.ai/learn/nptel/110107146/f525e7e86e85) (YouTube)
50. [Spinor Fields Path Integral](https://invisiblenetwork.ai/learn/nptel/110107146/7e3c392c0911) (YouTube)
51. [Gauge Fields (1)](https://invisiblenetwork.ai/learn/nptel/110107146/62d3281d191f) (YouTube)
52. [Gauge Fields (2)](https://invisiblenetwork.ai/learn/nptel/110107146/ca287cdd9a5e) (YouTube)
53. [Ito Equation, Stock Price Modelling](https://invisiblenetwork.ai/learn/nptel/110107146/0c72348baf45) (YouTube)
54. [Financial Derivatives](https://invisiblenetwork.ai/learn/nptel/110107146/0e09e764f854) (YouTube)
55. [Properties Of Options](https://invisiblenetwork.ai/learn/nptel/110107146/97045e8c1623) (YouTube)
56. [Pricing Of Options: Binomial Model (1)](https://invisiblenetwork.ai/learn/nptel/110107146/c19e7e727007) (YouTube)
57. [Pricing Of Options: Binomial Model (2)](https://invisiblenetwork.ai/learn/nptel/110107146/6f4f5795952b) (YouTube)
58. [Black Scholes Model](https://invisiblenetwork.ai/learn/nptel/110107146/83a6ca61a34d) (YouTube)
59. [Path Integral Solution Of Black Scholes Pde](https://invisiblenetwork.ai/learn/nptel/110107146/8d8b690ab04c) (YouTube)
60. [Misc Financial Applications Of Path Integrals](https://invisiblenetwork.ai/learn/nptel/110107146/d3fef6213b6d) (YouTube)