Perturbation Theory

Quantum Field Theory · Part 3

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Table of Contents

  1. 1.6.1 Connected vs Disconnected Diagrams
  2. 2.6.2 Vacuum Bubbles
  3. 3.6.3 Linked Cluster Theorem
  4. 4.Linked Cluster Theorem
  5. 5.Key Concepts (This Page)

Key Equations

$$Z[J] = e^{iW[J]} \quad \Rightarrow \quad W[J] = -i\ln Z[J]$$
$$Z[0] = \langle 0|0\rangle = \int \mathcal{D}\phi \, e^{iS[\phi]} = e^{i\Gamma_{\text{vac}}}$$
$$\langle 0|T\{\phi(x_1)\cdots\phi(x_n)\}|0\rangle = \frac{1}{Z[0]}\frac{\delta^n Z[J]}{\delta J(x_1)\cdots\delta J(x_n)}\Bigg|_{J=0}$$
$$\langle f|S - \mathbb{1}|i\rangle = \text{(sum of connected, amputated diagrams)}$$

Equations are rendered with MathJax in the PDF with professional LaTeX typesetting.

Course Context

This PDF is part of the Quantum Field Theory course on CoursesHub.World. A comprehensive graduate-level course in quantum field theory. Covers classical field theory, canonical quantization, path integrals, gauge theories, renormalization, the Standard Model, and advanced ...

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