Advanced Quantum Mechanics of Relativistic Particles

Relativistic quantum mechanics: Dirac equation and its applications,

introduction to the formalism of Quantum Field Theory, foundations of

Quantum Electrodynamics.

Program:

1. The Dirac equation: construction, interpretation, free solutions, hydrogen atom, non-relativistic limit.

2. Canonical formalism and free field quantization: scalar field, Dirac field, electromagnetic field.

3. Quantum Electrodynamics.

4. S-matrix, cross sections, lifetimes.

5. Perturbation theory, Feynman diagrams.

1. J.D. Bjorken, S.D. Drell, „Relativistic Quantum Mechanics”

2. S. Pokorski, "Gauge field theories"

3. M.E. Peskin, D.V. Schroeder, "An Introduction to Quantum Field Theory"

4. S. Weinberg, , „The Quantum Theory of Fields”, Vol. 1.

5. V. Radovanović, "Problem Book in Quantum Field Theory"

The student receives fundamental knowledge on the relativistic Dirac equation, Quantum Electrodynamics and other quantum field theories. He/she is able to solve the Dirac equation in simple potentials, calculate tree-level Feynman diagrams with fermions, scalars and gauge bosons, determine differential and total cross-sections for scattering processes, as well as lifetimes of unstable particles.

Two written tests during the semester. Written and oral final exams.

To take the oral exam, the student must have received 50% of points either from both written tests (together) or from one the written exams. The final mark depends on results from the tests, the written exam, as well as on the performance at the oral exam.

Participation in classes is strongly encouraged. It is believed to help pass the course.