Correlation Functions

Quantum Field Theory · Part 3

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Table of Contents

  1. 1.4.1 What Are Correlation Functions?
  2. 2.4.2 Path Integral Formula
  3. 3.4.3 Free Field Theory
  4. 4.4.4 Connected vs Disconnected
  5. 5.4.5 Momentum Space
  6. 6.4.6 Physical Interpretation
  7. 7.2-Point Function
  8. 8.4-Point Function
  9. 9.Odd Point Functions
  10. 10.LSZ Connection to S-Matrix

Key Equations

$$\boxed{G^{(n)}(x_1,\ldots,x_n) = \langle 0|T\{\phi(x_1)\cdots\phi(x_n)\}|0\rangle}$$
$$\boxed{G^{(n)}(x_1,\ldots,x_n) = \frac{1}{Z[0]}\int \mathcal{D}\phi \, \phi(x_1)\cdots\phi(x_n) \, e^{iS[\phi]}}$$
$$G^{(2n+1)} = 0 \quad \text{(all odd point functions vanish)}$$
$$\tilde{G}^{(n)}(p_1,\ldots,p_n) = \int \prod_{i=1}^n d^4x_i \, e^{ip_i \cdot x_i} G^{(n)}(x_1,\ldots,x_n)$$

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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