Non-Relativistic Quantum Field Theory

Non-Relativistic Quantum Field Theory
Outline of 15 lectures (M. Stone, The Physics of Quantum Fields)
1. Introduction:
• Overview of approaches to the many-body problem
• QFT as a many-body theory
2. Electrons in solids I (S. 9.1 – 9.2.3 + notes)
• Fermi gas & Fermi Liquid
3. Electrons in solids II (9.2.4 – 9.3 + notes)
• Fermi gas & Fermi Liquid
• Electron – fonon interaction
4. Non-Relativistic Bosons I (10.1 – 10.2 + notes)
• Order parameter
• Mean field theory
• Superfluidity
5. Non-Relativistic Bosons II (10.3 – 10.4)
• The dilute Bose gas
6. Application to cold atomic gases (notes)
7. QFT at finite temperature (11)
• Matsubara sums
• Free Bose & Fermi gases
8. Superconductivity (14.3)
• Order parameter,
• Mean field theory,
• Effective action
9. Systematics of mean-field theory (notes)
• Hubard-Stratonovich transformation
• Hartree and Hartree-Fock
• Anomalous terms
• The concept of quantum phase transition
10. Introduction to RG (16)
(repetition of material from Statistical Physics II)
• Blockspin methods
• Fixed points
• Flows
11. QFT approach to RG I (17.1 - 17.3)
• Gaussion fixed point
12. QFT approach to RG II (17.4 – 17.5)

• Non-linear sigma model;
• phi^4-theory
13. QFT approach to RG III (Notes)
• Fermi Liquid theory
• Superconductivity.
14. Lattice field theory I (15.1 – 15.2)
• basic ideas
15. Lattice field theory II (15.3)
• continuum limit