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. Free online course in Quantum Field Theory (QFT). 8 parts covering classical field theory, canonical quantization, path integrals, QED, non-Abelian gauge theories, renormalization, the Standard Model,...

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