Lagrangian Formalism

Quantum Field Theory · Part 1

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Table of Contents

  1. 1.1.1 Review: Lagrangian Mechanics for Particles
  2. 2.1.2 From Discrete to Continuous Systems
  3. 3.1.3 Relativistic Field Theory
  4. 4.Hamilton's Principle
  5. 5.Canonical Momentum
  6. 6.Hamiltonian
  7. 7.Continuum Limit
  8. 8.Field Lagrangian
  9. 9.Lorentz Covariance
  10. 10.Invariant Interval

Key Equations

$$L(q^i, \dot{q}^i, t) = T - V$$
$$H(q^i, p_i, t) = \sum_i p_i \dot{q}^i - L$$
$$\sum_{n=1}^N (\cdots) a \to \int_0^L (\cdots) dx$$
$$\rho \frac{\partial^2 \phi}{\partial t^2} = \mu \frac{\partial^2 \phi}{\partial x^2}$$

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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