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  תורת שדות לחומר מעובה
  Condensed matter field theory                                                                        
0321-4285
מדעים מדויקים | פיסיקה ואסטרונומיה
קבוצה 01
סמ'  ב'1200-1500104שנקר - פיזיקהשיעור ד"ר אילן רוני
ש"ס:  3.0

סילבוס מקוצר

*Canonical quantization, Zero temperature Green functions, Perturbation theory at zero temperature, Feynman diagrams, Finite-temperature Green functions and Matsubara representation, Path integrals, Instantons, functional integrals for Bosons and fermions, Anomalous Green functions and systems with broken symmetry. Non-Equilibrium and Keldysh formalism.  Applications: Landau Fermi liquid, Ising model, Majorana and Dirac fermions. 

 

*Tentative syllabus. Most topics are expected to be covered, slight changes are possible due to time constraints

Course description

Condensed Matter Field Theory Syllabus

Dr. Roni Ilan

Email :ronilan@tauex.tau.ac.il

Academic Year, Semesters

2018, 2nd semester

Number of Hours/ Credits :3

Mandatory/Elective:

Elective

  Course overview – short abstract

Introductory course for graduate students that focuses of field theoretic methods in condensed matter. Starting from second quantization, the course introduces quantum fields theory, Green’s functions and zero and finite temperature, perturbative methods and diagrammatic techniques, and the basics of path integrals. The connection with response functions and statistical mechanics will be made.

 Familiarizing the students with the formalism of QFT for condensed matter.

Assessment: coursework and grade structure

Assignments – 20%

Student talks– 20%

Final exam – 60%

Tentative Week-by-week content, assignments and reading

Week 1: Overview, canonical quantization and second quantization recap.

Week 2: Zero temperature Green functions, from single particles to quantum fields. Interaction picture.

Week 3: Retarded and advances functions, the Lymann representation.

Week 4: Adiabatic theory and the Gell-Mann low theorem.

Week 5: Zero temperature perturbation theory, Wick’s theorem

Week 6: Feynman diagrams at zero temperature

Week 7: Finite temperature Green’s functions, connection with statistical mechanics. Integration picture in imaginary time.

Week 8: Finite temperature Green’s functions, Matsubara formalism

 Week 9: Perturbation theory at finite temperature, Matsubara sums

 Week 10: Link between temperature Green’s functions, retarded response

 Week 11: Path integrals, functional field integrals for Bosons and Fermions

 Week 12: Basics of Fermi liquid theory, RPA

  Week 13: Student presentations

There will be home assignments and reading assignments throughout the course. Home assignments will not be graded, full marks will be given to assignments submitted in a satisfactory manner. 

Main textbooks

We will use several canonical texbooks throughout the course, switching between them as needed according to topics that are covered best in each textbook. 


Methods of Quantum Field Theory in Statistical Physics/ I. E. Dzyaloshinski, L. P. Gorkov, A. A. Abrikosov

 Quantum Theory of Many-Particle Systems/Fetter and Walecka

Many-Body Quantum Theory in Condensed Matter Physics/ Bruus and Felnsberg

 Introduction to many body physics/Piers Coleman

 Condensed matter field theory/Altland and Simons

Other references

 An Introduction To Quantum Field Theory/Peskin and Schroeder

 

 

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