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Course: Relativistic quantum theory

Department/Abbreviation: SLO/PGS8R

Year: 2021

Guarantee: 'Mgr. Jiří Kvita, Ph.D.'

Annotation: Students are assumed to master the topics described in the content of the subject.

Course review:
The goal is to present the principles of the relativistic quantum mechanics and quantum field theory in application to scattering in high energy physics. 1. Review of relevant parts of the non-relativistic quantum mechanics, perturbation and scattering theory. 2. Symmetries: rotation and Lorentz groups. 3. Relativistic wave equation: Klein-Gordon equation and its solutions. 4. Dirac equation, free particle, non-relativistic limit. 5. Symmetries of the Dirac equation, projection operators to energy and spin eigenstates. 6. Particle in the electromagnetic field, Klein paradox. 7. Least action principle, classical motion, relativistic particle, EM field as infinite degree system. 8. Noether theorem, symmetries and conservation laws. 9. Quantization of the field: normal ordering, Fock space, scalar field, charge, antiparticles, time ordering, Green functions. 10. Quantization of the Dirac, EM and Proca fields. 11. Wick theorem, perturbative S-matrix expansion, Dyson series. 12. Application on the phi^4 theory, Feynman diagrams, Yukawa theory, decays. 13. Quantum electrodynamics, electron-positron annihilation to a muon-antimuon pair, Compton and bremsstrahlung processes. 14. Notion of the regularization and renormalization.