Quantum Field Theory and Many Body Physics 2020
Class will be online only!
For participation, please register in Campus Management ahead of April 20 - including your email address! Otherwise, I have no way of inviting you to the meetings and you will not be able to access the online material.
Lectures are available as videos and lecture notes, and will be assigned on a weekly basis. Online meetings will be held Mo 10-12 and Th 10-12 (starting April 20) for question-and-answer and discussion sessions.
In addition, there will be online tutorials Fr 10-12 (starting April 24).
Problem sets will be made available on Thursdays and have to be turned in electronically by the following Thursday at 10am at the latest.
EXAM:
1) The grade will be based on a 15min presentation on an (assigned) paper followed by 15min of questions on the paper and other class content (all online). (You can opt out of this and insist on a written exam. However, this would have to be postponed until better times.)
2) The exams will take place on Mo August 3 and Tu August 4. The topics for the presentation will be distributed among the participants by random number generator during the lecture on July 13.
3) Please communicate by email by July 6 if you intend to participate in the exam.
Problem sets
Set 1 (due April 30) Solution
Set 2 (problem 1: due ahead of every lecture; problem 2-4: due May 7) Solution
Set 3 (due May 14; video summaries ahead of every lecture) Solution
Set 4 (due May 21; video summaries ahead of every lecture) Solution
Set 5 (due May 28; video summaries ahead of every lecture) Solution
Set 6 (due June 4; video summaries ahead of every lecture) Solution
Set 7 (due June 11; video summaries ahead of every lecture) Solution
Set 8 (due June 18; video summaries ahead of every lecture) Solution
Set 9 (due June 25; video summaries ahead of every lecture) Solution
Set 10 (due July 2; video summaries ahead of every lecture) Solution
Set 11 (due July 9; video summaries ahead of every lecture) Solution
Video lectures and lecture notes
Chapter 1: Landau Theory of Phase Transitions (bonus material)
- Phenomenology of phase transitions Th April 23
- Review of statistical mechanics (paramagnets) Th April 23
- Mean field theory for the Ising model Th April 23
- Landau theory of phase transitions Fr April 24
- Hubbard-Stratonovich transformation Fr April 24
- Order parameter fluctuations Fr April 24
Chapter 2: Quantum Phase Transitions
- Transverse field Ising model Mo April 27
- Duality transformation Mo April 27
- Jordan-Wigner transformation Mo April 27
- Bogoliubov transformation Th April 30
- Phases of the free-fermion model Th April 30
Chapter 3: Free bosonic fields: harmonic chain
- Model and classical solution Mo May 4
- Hamiltonian fomulation Mo May 4
- Statistical mechanics of the harmonic chain Th May 7
- Functional integrals and source fields Th May 7
Chapter 4: Path integrals
- Propagator Mo May 11
- Path integral in quantum mechanics Mo May 11
- Imaginary time path integral for partition function Mo May 11
- Path integral for the harmonic chain Th May 14
Chapter 5: Green functions and linear response
- Kubo formula Th May 14
- Lehmann representation I Mo May 18
- Lehmann representation II Mo May 18
- Linear response and dissipation Mo May 18
Chapter 6: Boson functional integral
- Coherent states and path integrals Mo May 25
- Functional integrals for bosonic many particle systems Mo May 25
Chapter 7: Interacting Bose systems
- Bose-Einstein condensation Th May 28
- Weakly interacting bosons Th May 28
- Low-energy effective action Th May 28
- Physical observables Th Jun 4
- Quantum fluctuations in finite systems Th Jun 4
- Quantum fluctuations in 1+1 dimensions Th Jun 4
- Quantum fluctuations in 2+1 dimensions Th Jun 4
- dc Josephson effect Th Jun 4
Chapter 8: Boson superfluidity
- Action and gauge invariance Mo Jun 8
- Electromagnetic response Mo Jun 8
- Anderson-Higgs mechanism Mo Jun 8
Chapter 9: Bosons at finite temperatures
- Dimensional analysis Th Jun 11
- Bosons at finite temperatures Th Jun 11
- Vortices and Kosterlitz-Thouless transition Th Jun 11
- Coulomb gas model Mo Jun 15
- Real space renormalization Mo Jun 15
- RG flow Mo Jun 15
Chapter 10: Fermion functional integrals
- Grassmann variables Th Jun 18
- Fermion coherent states Th Jun 18
- Gaussian integrals Mo Jun 22
- Coherent state functional integrals for fermions Mo Jun 22
Chapter 11: Random-phase approximation
- Jellium model and screening Th Jun 25
- Hubbard-Stratonovich and effective action Th Jun 25
- Random phase approximation Mo Jun 29
- RPA and source fields Mo Jun 29
Chapter 12: BCS theory
- Effective action Th Jul 2
- Gap equation Th Jul 2
- Condensation energy Th Jul 2
- Ginzburg-Landau theory I Mo Jul 6
- Ginzburg-Landau theory II Mo Jul 6
Chapter 13: Feynman diagrams: Thermodynamic potential
- Perturbation theory for the partition function Th Jul 9
- Feynman rule Th Jul 9
- Thermodynamic potential Th Jul 9
- Frequency and momentum representation Mo Jul 13
Chapter 14: Feynman diagrams: Green functions
- Feynman rules and Green functions Mo Jul 13
- Self energy and Dyson equation Th Jul 16
- Hartree-Fock approximation Th Jul 16
- Lifetime in the jellium model Th Jul 16