from Feynman Diagrams, Loop expansions, Limiting behavior, Saddle point
approximation, Effective field,
Renormalization, 1-D field theory, Feynman Rules & SDE, propagator, SDE in
terms of propagators, Explicit expression for propagator, Generalization to
D-dimensions, Continuum limits.
Week 9:Mode space computations, divergences, loop integrals, Generatingfunctionals, correlators and allied results in D- Dimensional Euclidean space; Field theory in Minkowski space, Scalar field generating functional.
Week 10:Scalar field propagator & correlators, Fourier integrals, Causality, Interacting field in Minkowski space, Important identities, Derivation of SDE,Fermionic fields & their path integral quantization.
Week 11:Maxwell equations & gauge field quantization, their path integral. Fluctuation properties offinancial assets, Brownian motion & Ito’s lemma; Lognormal distribution & stock price distribution, Formulation of & solution to the Fokker Planck equation for stock price model.
Week 12:Basic theory of options; Profit diagrams; Put-Call parity; Option pricing, the Binomial &Black Scholes Models;Risk Neutral valuation; American options; Derivation of and solution to the Black-Scholes PDE; Path integral approach to pricing of path independent options; Path integral valauation of other cash flow structures e.g. zero coupon bonds etc..