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Canonical Quantization of QFT
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Module 6
Path Integral Formulation of Quantum Field Theory
1
Path Integral for Propagators: Time-Slicing Derivation
Derive the path integral representation for the quantum mechanical propagator using the time-slicing method.
2
Path Integrals in Scalar Field Theory
Extend the path integral formalism to scalar field theory to define the generating functional for Green's functions.
3
Feynman Propagator from the Generating Functional
Derive the Feynman propagator for a scalar field from the generating functional.
4
Functional Derivatives and Correlation Functions
Compute correlation functions by taking functional derivatives of the generating functional.
5
Grassmann Numbers and Berezin Integration
Define Grassmann numbers and the Berezin integral for their integration.
6
Path Integral for Free Dirac Fields with Grassmann Variables
Construct the path integral for the free Dirac field using Grassmann variables.
7
Feynman Rules from Path Integrals and the S-Matrix
Relate the generating functional in the presence of external sources to the S-matrix and derive Feynman rules from the path integral.
8
Euclidean QFT and Statistical Mechanics Duality
Explain the relationship between quantum field theory in Euclidean spacetime and statistical mechanics.
Previous module
Radiative Corrections and Renormalization in QED
Next module
Non-Abelian Gauge Theories and QCD