PHY 510 Advanced Quantum Mechanics (Relativistic)

Semester: Fall (alternate years)
Credit Hours: 4
Prerequisite: PHY 407, PHY 408, or equivalent

Review of Dirac equation, covariance and transformation properties of the Dirac equation, propagator theory, applications, second order corrections and renormalization, Klein Gordon equation, non-electromagnetic interactions.

syllabus

1. Special Relativity and Quantum Mechanics. Lorentz transformations, representations on plane waves, angular momentum and spin, 0(3,1) algebra, Dirac spinors for spin 1/2, probability current, normalization, mass zero cases.
2. Scattering Theory. Lorentz transformations of rates and cross sections; interaction picture, S + T matrices, invariant amplitudes, covariant perturbation theory. Example of Coulomb scattering.
3. Relativistic Equations and Quantum Fields. Klein-Gordon and Dirac equations, negative energy solutions and antiparticles, interaction with EM field; applications of Dirac equation to atomic problem, anomalous moments, strong fields; covariant formulation of Dirac theory. Canonical quantization of Klein-Gordon and Dirac fields.
4. Quantum Theory of Electromagnetic radiation. Free fields, plane wave expansion, gauge and transversality, interaction with charged systems.
5. Quantum Electrodynamics to Second Order. Feynman propagator theory, spin sums; applications to Compton scattering, pair creation/annihilation, Mott, Moller, and Bhabba scattering.
6. Symmetries and Weak Interactions. Weak interactions and P, C. T. symmetries; V-A theory with vector bosons, quarks and leptons; effective hadron theory.
7. Feynman Rules and Higher Orders; Renormalization. General Feynman rules; introduction to the phenomena and problems of higher order processes; renormalization.

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