Physics Doctoral Program (Ph.D., 3,5 - 5 Years)

The student agrees on a dissertation topic with an adviser from among the faculty members of the Physics Department, preferably within the first two semesters. An original work required in the field of study. The dissertation should include an introduction part covering the theory and literature on the topic, original research part, results, discussion part, and a conclusion of the dissertation. For the thesis to be defended, the student must have at least three successful thesis monitoring reports. The dissertation must be defended under oral examination conditions.

Initial value problems in advanced physics. Nonlinear Flow and Conservation Laws. Hilbert space and linear operators. Group theory. Tensors. Advanced Variation Principle for Spacetimes.

Variational principles of mechanics. Noether’s theorem and conserved quantities in mechanics. Continuum mechanics and field theory. Chaos. Hamilton-Jacobi analysis of relativistic motions.

Review of Special Theory of Relativity and Lorentz invariance. Lagrangian and covariant formulation of the Maxwell equations. Field and Stress-Energy tensors. Transformation rules of Electric and Magnetic fields under motion. Lienard- Wiechert potentials, radiation from moving charges and radiation reaction. Electromagnetic plane waves and time harmonic currents in multipole expansion.

Collision theory, scattering cross-section, optical theorem, Born approximation, resonances, S-matrix. Relativistic quantum mechanics, Klein-Gordon equation, spinors, Dirac equation, relativistic invariance. Introduction to second quantization.

Ph.D. Qualifying Exam