Concept Focus

Path Integrals

Path integrals, sum over histories, generating functionals, and the route from sources to correlators.

Overview

The path integral rewrites amplitudes as a sum over histories weighted by a phase. In field theory, that becomes an integral over field configurations, and with sources added it becomes the generating machine for correlation functions and perturbation theory.

This concept page captures searches around path integral intuition, QED path integral setup, and the source formalism that leads to Feynman diagrams.

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Related Lessons

Lesson 15

Path Integrals

A full lecture reconstruction introducing path integrals as a Lagrangian reformulation of quantum mechanics, starting from the Feynman–Hibbs phase-space path integral, then developing coherent-state path integrals for bosons and Grassmann coherent-state path integrals for fermions as preparation for Lagrangian perturbation theory in QFT.

Lesson 16

The QED Path Integral

A full lecture reconstruction showing how bosonic and fermionic coherent-state path integrals combine into the QED generating functional, and how changes of variables turn the Coulomb-gauge Hamiltonian path integral into a manifestly Lorentz-invariant Maxwell–Dirac action with sources.

Lesson 17

Feynman Diagrams

A full lecture reconstruction showing how Lorentz-invariant perturbative QED emerges from the QED path integral as variational calculus on a Gaussian generating functional, and how the surviving terms organize into Feynman diagrams and Feynman rules.

Interactive Visualizations

Animation

Path Integral as Sum Over Histories

Start with many particle paths between fixed endpoints, weight each by e^{iS}, watch interference select the stationary path, then generalize the same idea to a sum over field configurations.

Animation

Generating Functional and Source Trick

Introduce a source J(x), differentiate the generating functional to pull down field insertions, and watch correlators and diagrams emerge from one master object.