Lecturer:
Associate professor John Ove Fjærestad (office: E5-126, email: john.fjaerestad@ntnu.no, phone: 93448)
Contents:
Klein-Gordon and Dirac equation. Field quantization. Occupation number representation for nonrelativistic fermionic and bosonic many-particle systems. Interacting electron gas. Lattice models for fermions and spins. Spin-wave theory of ferro- and antiferromagnets. Symmetries and conserved quantities. Broken symmetries, Goldstone modes. Green functions. Matsubara formalism. Many-particle perturbation theory and Feynman diagrams. Various applications.
Lectures:
Tuesdays 10:15-12:00 and Thursdays 9:15-10:00 in E5-103.
Tutorials:
Thursdays 8:15-9:00 in E5-103 (starting in week 4).
As a pre-exam requirement, each student will present solutions to one or more tutorial problems
at at least one tutorial (more details will be provided later).
Reference group:
Espen Auseth Nielsen (espenani@stud.ntnu.no)
NN (one more student needed)
Resources:
Main resources:
Notes by the lecturer (will be made available on the website as the course progresses).
Supporting resources:
There is no single textbook that covers all the material that will be discussed in the course. Much of the material on non-relativistic quantum many-particle systems is covered in "Many-body quantum theory in condensed matter physics" by Bruus and Flensberg (Oxford, 2004), which is the main recommended textbook for this part of the course. Other recent textbooks in the same area that may be useful are "Condensed matter field theory" by Altland and Simons (2nd ed., Cambridge, 2010) and
"Introduction to many body physics" by Piers Coleman (Cambridge, 2012; a pre-publication copy is available here). An old
classic is "Quantum theory of many-particle systems" by Fetter and Walecka from 1971 which is available in a non-expensive paperback version (Dover, 2003). The main reference on the quantum magnetism material is "Interacting electrons and quantum magnetism" by Auerbach (Springer, 1994).
In the last part of the course we plan to discuss some relativistic systems. The main reference for that part will be "Quantum theory of many-particle systems", lecture notes for TFY4210, 2nd ed., 2011, by J. O. Andersen. Other references will be provided later.
Lecture notes etc.:
(please let me know if you find errors, typos, or unclear statements in the notes)
Second quantization
Second quantization representation for the Hamiltonian of an interacting electron gas
Noninteracting electrons. The free electron gas
Electrons in a crystal: Bloch and Wannier states (in preparation), tight-binding model (in preparation; 2012 version)
The Hubbard and Heisenberg models (in preparation; 2012 version)
Spin-wave theory of ferro- and antiferromagnets (in preparation; 2012 version)
Transformations and symmetries in quantum mechanics
Symmetry breaking (in preparation; 2012 version)
Introduction to Green functions and many-body perturbation theory (may be updated later)
About impurity (self-)averaging (from Bruus and Flensberg)
Tutorial sets:
| Tutorial | Date | Presenter | Problems | Solution |
|---|---|---|---|---|
| 1 | 24 Jan | Tobias Grøsfjeld | |
|
| 2 | 31 Jan | Oladunjoye Awoga | |
|
| 3 | 07 Feb | --- | |
|
| 4 | 14 Feb | Espen Auseth Nielsen | |
|
| 5 | 21 Feb | --- | |
|
| 6 | 28 Feb | Espen Undheim | |
|
| 7 | 07 Mar | Runar Skålbones | |
|
| 8 | 14 Mar | --- | |
|
| 9 | 21 Mar | Ravinder Gill | |
|
| 10 | 11 Apr | --- | |
|
| 11 | 18 Apr | Magnus Eik | |
|
| 12 | 30 Apr | Felix Prinz | |
|
Other:
Past exams
2012 course website