Condensed Matter Theory 1 (CMT1)

Skills

Participants are expected to learn to:

• Describe an interacting quantum mechanical many-particle system by the use of second quantization.

• Handle (for example (anti)commuting mixed products of) boson and fermion quantum field operators in various representations (Schrodinger, Heisenberg, and the interaction picture).

• Use real-time and Matsubara Green functions to solve interacting many-body problems.

• Use mean-field theory to simplify interacting Hamiltonians to simpler manageable problems.

• Use equation of motions techniques to obtain Greens functions.

• Derive and use Feynman rules for perturbation theory within potential scattering, electron-electron, and electron-phonon interactions.

• Perform a detailed calculation and regularization of the ground state energy for the interacting electron gas including the screening of long-range Coulomb interactions and its Landau damped plasmons.

• Describe single-particle excitations in an interacting many-particle system in terms of renormalized quasi-particles. This includes being able to obtain effective masse and charge, Fermi surfaces, Z-factors and lifetimes.

• To use all these acquired skills to solve relevant physics problems, including mainly issues within the physics of solid materials, quantum liquids and ultracold atomic gasses.

Knowledge
In the course, we focus on the interacting electron gas, describing metals and semiconductors, and use this as an example to illustrate the techniques taught. The course is meant to teach the fundamental field-theoretical concepts and techniques such as second quantization, equations of motion for operators, many-particle Green functions at finite temperatures, and Feynman diagrams.

Competences
This course will provide the students with the required background for further studies within this research field, i.e. the course CMT2 or a master thesis. The course will provide most of the modern formalism used in the scientific literature on condensed matter physics.