Finite Temperature

Quantum Field Theory · Part 7

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Table of Contents

  1. 1.4.1 Thermal Density Matrix
  2. 2.4.2 Imaginary Time Formalism
  3. 3.4.3 Matsubara Frequencies
  4. 4.4.4 Thermal Propagators
  5. 5.4.5 Thermal Distributions
  6. 6.4.6 Finite Temperature Effective Potential
  7. 7.4.7 Thermal Phase Transitions
  8. 8.4.8 First vs Second Order Transitions
  9. 9.4.9 Phase Transitions in the Early Universe
  10. 10.4.10 Baryogenesis and Sakharov Conditions

Key Equations

$$\rho = \frac{1}{Z} e^{-\beta H}$$
$$e^{-\beta H} = e^{-iH(i\beta)} = e^{-iHt}\Big|_{t \to -i\beta}$$
$$i\omega_n \to \omega + i\epsilon$$
$$n_B(\omega) \approx \frac{T}{\omega}, \quad n_F(\omega) \approx \frac{1}{2} - \frac{\omega}{4T}$$

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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