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תורת שדות לחומר מעובה
Condensed matter field theory |
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*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
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