Nonlinear Bosonization of Fermi Surfaces - The Method of Coadjoint Orbits

Explore a comprehensive lecture on the nonlinear bosonization of Fermi surfaces using the method of coadjoint orbits. Delve into a field-theoretical reformulation of Landau Fermi liquid theory, where systems with Fermi surfaces are described as coadjoint orbits of the group of canonical transformations. Discover how this approach naturally leads to nonlinear bosonization and learn about the Berry phase acquired by Fermi surfaces when changing shape. Examine the resulting local effective field theory that captures both linear and nonlinear effects in Landau's Fermi liquid theory. Gain insights into possible extensions and applications of this theory, referencing work by Luca Delacrétaz, Umang Mehta, Yi-Hsien Du, and Dam T. Son. Follow the lecture's progression through topics such as Landau's theory, Landau parameters, previous approaches, the dual space, coadjoint group actions, reference states, quadratic order, three-point functions, and more.

Intro
Outline
Landaus Theory
Landau Parameters
Perm Liquid Theory
Previous Approaches
Problem
Main Idea
The Dual Space
Coadjoint Group Actions
Reference State
The very phase
Quadratic order
Threepoint function
Conclusion
Questions
Quantum Mechanical
Wilsonian Renewalization
Theta