S Matrix

Quantum Field Theory · Part 3

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Table of Contents

  1. 1.1.1 Why Do We Need Interactions?
  2. 2.1.2 Interacting Lagrangian
  3. 3.1.3 Interaction Picture
  4. 4.1.4 Time Evolution Operator
  5. 5.1.5 The S-Matrix (Scattering Matrix)
  6. 6.1.6 Dyson Series (Perturbative Expansion)
  7. 7.1.7 LSZ Reduction Formula
  8. 8.Properties of S-Matrix
  9. 9.🎯 Key Takeaways

Key Equations

$$\boxed{\mathcal{L} = \mathcal{L}_0 + \mathcal{L}_{\text{int}}}$$
$$|\psi_I(t)\rangle = U(t,t_0)|\psi_I(t_0)\rangle$$
$$T[A(t_1)B(t_2)] = \begin{cases} A(t_1)B(t_2) & t_1 > t_2 \\ B(t_2)A(t_1) & t_2 > t_1 \end{cases}$$
$$\boxed{S_{fi} = \langle f|S|i\rangle}$$

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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