Duke Physics

Graduate Advanced Physics (PHY 322)

Course description:

Dirac equation, canonical field quantization, gauge symmetries, electromagnetic field quantization, identical particles and second quantization, symmetry breaking, gases of interacting bosons and fermions, interaction of quantized radiation field with atoms, Rayleigh scattering, Thomson scattering, nonlinear optical processes, and special topics.

Possible principal texts:

1. E. Merzbacher, Quantum Mechanics, 3^rd ed., (1997).
2. Greiner and Mueller, Quantum Mechanics: symmetries, (2004).
3. C. A. Brau, Modern Problems in Classical Electrodynamics, (Oxford Univ. Press, 2004).
4. Pathria, Statistical Mechanics, 2^nd ed. (Elsevier, 1996).
5. C. Cohen-Tannoudji et al., Quantum Mechanics, 2^nd ed. (2006).

Other texts to consider:

1. J. J. Sakurai, Advanced Quantum Mechanics, (1967).
2. M. Peskin and D. Schroeder, Quantum Field theory, (1995).
3. E. M. Lifshitz and L. Pitaevskii, Statistical Physics, part 2, from the Landau and Lifshitz series, vol. 9 (1980).
4. R. Loudon, The quantum theory of light, 3^rd ed., (Oxford, 2000).
5. L. D. Landau and E. Lifschitz, Electrodynamics of Continuous Media (vol. 8).

Prerequisites

The prerequisites are PHY 311 and PHY 312.

Syllabus

• Canonical field quantization.
• Dirac equation.
• Quantization of EM field in radiation gauge, coherent states.
• Density matrix.
• Second quantization for bosons, weakly interacting Bose gas, low energy excitations.
• Second quantization for fermions, weakly interacting Fermi gas.
• Gauge symmetries: U(1), SU(2), SU(3), symmetry breaking, Goldstone bosons, Higgs mechanism.
• Interaction of radiation with atoms, Rayleigh and Thomson scattering.
• Microscopic theory of dielectric function
• Microscopic theory of magnetism: exchange coupling, Hubbard model, Heisenberg model, spin waves.
• Nonlinear materials: multiphoton processes, Raman scattering.