Lectures: March 28 - June 1
When: Tuesday, 9:00 am - 11:50 am & Thursday 9:00 am - 9:50 am
Where: Room: F160, Tech Institute

Symmetry and topology play special roles in atomic, nuclear, high-energy and condensed matter physics. This is the second of a two-quarter sequence on Symmetry, topology and geometry in physics. This quarter can be taken independently of the 1st quarter provided the student has basic familiarity with the continuous groups, SO(3) and SU(2), that play key roles in quantum mechanics. The second quarter will explore the role of spontaneous symmetry breaking (SSB) in theories ranging from phase transitions to mass generation in quantum field theory, particularly as SSB relates to the emergence of new elementary quanta, as well as novel excitations, "topological defects". We will develop homotopy theory related to the underlying topology of broken symmetry ground states and use it to classify and study the stable topological defects in a wide range of broken symmetry states of condensed matter and quantum field theories.

Syllabus

• Symmetry, Symmetry Breaking & Phase transitions
• Landau Theory and Lagrangian Field Theories
• Discrete Symmetries: Parity, Time-Reversal & Charge Conjugation
• More on Lie Groups and their Representations
• Direct Product Spaces - Reducible representations
• Topology, Homotopy Groups and Topological Defects
• Applications in Condensed Matter and Quantum Field Theories
  • CMP: Crystals, Liquid Crystals, Ferromagnets and Superconductors
  • QFT: Mass Generation, Higgs and Gauge Bosons
  • CMP: Higgs Bosons and the Topology of Superfluid Helium-Three
  • QFT/CMP: Nucleation of Topological Defects out of Equilibrium

1. Topological Theory of Defects in Ordered Media, N. D. Mermin, Rev. Mod. Phys. 51, 594 (1979).
2. Cosmic Strings and Other Topological Defects, A. Velinkin and E. Shellard, Cambridge University Press.
3. J.-C. Tolèdano and P. Tolèdano, The Landau Theory of Phase Transitions, World Scientific.
4. L. D. Landau and I. M. Lifshitz, Statistical Physics, Volume 5, Course in Theoretical Physics, Pergamon Press, 1969.
5. Topological Defects & Non-equilibrium Dynamics of Symmetry-Breaking Phase Transitions, Eds. Y. Bunkov and H. Godfrin, Kluwer Academic Publishers, 2000.
6. Group Theory in a Nutshell, A. Zee, Princton Press.