IAS CMP/QFT Group Meeting

Abstract: I will discuss effective field theory approaches to quantum matter, focusing on Fermi liquids and quantum Hall systems. For Fermi liquids, low-energy fluctuations can be organized by area-preserving deformations in phase space, leading to a nonlinear bosonized description of the Fermi surface. Magnetic fields and Berry curvature can be incorporated through a generalized symplectic structure, providing a unified framework for nonlinear response and collective phenomena. I will then discuss how quantization leads naturally to a noncommutative formulation in terms of the Moyal deformation or an equivalent operator language. Finally, I will connect this phase-space viewpoint to incompressible quantum Hall fluids, where related geometric structures organize collective excitations and quantum dynamics. Together, these examples illustrate how geometric and algebraic structures can provide a systematic framework for effective field theories of quantum many-body systems.