Path Integral Qm

Quantum Field Theory · Part 3

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Table of Contents

  1. 1.2.1 The Path Integral Idea
  2. 2.2.2 Transition Amplitude
  3. 3.2.3 Example: Free Particle
  4. 4.What Does "Sum Over All Paths" Mean?
  5. 5.Key Concepts (This Page)

Key Equations

$$\boxed{K(x_b,t_b;x_a,t_a) = \int \mathcal{D}x(t) \, e^{iS[x(t)]/\hbar}}$$
$$S[x(t)] = \int_{t_a}^{t_b} dt \, L(x,\dot{x},t) = \int_{t_a}^{t_b} dt \left[\frac{1}{2}m\dot{x}^2 - V(x)\right]$$
$$K(x_b,t_b;x_a,t_a) = \lim_{N\to\infty} \int dx_1 \cdots dx_{N-1} \prod_{j=0}^{N-1} \sqrt{\frac{m}{2\pi i\hbar \epsilon}} \exp\left[\frac{i}{\hbar}\epsilon L(x_j, \frac{x_{j+1}-x_j}{\epsilon})\right]$$
$$S[x(t)] = \int_{t_a}^{t_b} dt \, \frac{1}{2}m\dot{x}^2$$

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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