04416nam a22006375i 4500 978-3-031-72403-9 DE-He213 20251030113243.0 cr nn 008mamaa 241024s2024 sz | s |||| 0|eng d 9783031724039 978-3-031-72403-9 10.1007/978-3-031-72403-9 doi QC174.4-.43 PHQ bicssc SCI057000 bisacsh PHQ thema Mehta, Umang. author. aut http://id.loc.gov/vocabulary/relators/aut 86518 Postmodern Fermi Liquids [electronic resource] / by Umang Mehta. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XV, 102 p. 9 illus., 8 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Springer Theses, Recognizing Outstanding Ph.D. Research, 2190-5061 1 Introduction -- 2 Review and History of Fermi Liquid Theory -- 3 Postmodern Fermi Liquids -- 4 The Operator Algebra and the Hamiltonian Formalism -- 5 Effective Action from the Coadjoint Orbit Method -- 6 A Road to Perturbative Non-Fermi Liquids -- 7 Spin and BCS Extensions -- 8 Conclusion and Outlook. This thesis develops a new approach to Fermi liquids based on the mathematical formalism of coadjoint orbits, allowing Landau’s Fermi liquid theory to be recast in a simple and elegant way as a field theory. The theory of Fermi liquids is a cornerstone of condensed matter physics with many applications, but efforts to cast Landau’s Fermi liquid theory in the modern language of effective field theory suffer from technical and conceptual difficulties: the Fermi surface seems to defy a simple effective field theory description. This thesis reviews the recently-developed formalism for Fermi liquids that exploits an underlying structure described by the group of canonical transformations of a single particle phase space. This infinite-dimensional group governs the space of states of zero temperature Fermi liquids and allows one to write down a nonlinear, bosonized action that reproduces Landau’s kinetic theory in the classical limit. The thesis then describes how that Fermi liquid theory can essentially be thought of as a non-trivial representation of the Lie group of canonical transformations, bringing it within the fold of effective theories in many-body physics whose structure is determined by symmetries. After analyzing the benefits and limitations of this geometric formalism, pathways to extensions of the formalism to include superconducting and magnetic phases, as well as applications to the problem of non-Fermi liquids, are discussed. The thesis begins with a pedagogical review of Fermi liquid theory and concludes with a discussion on possible future directions for Fermi surface physics, and more broadly, the usefulness of diffeomorphism groups in condensed matter physics. Quantum statistics. 75355 Low temperatures. 78166 Mathematical physics. Topological groups. 72299 Lie groups. 72300 Quantum electrodynamics. 70514 Elementary particles (Physics). 68885 Quantum field theory. 68886 Quantum Fluids and Solids. 75356 Low Temperature Physics. 78169 Mathematical Physics. Topological Groups and Lie Groups. 72304 Quantum Electrodynamics, Relativistic and Many-body Calculations. 70517 Elementary Particles, Quantum Field Theory. 68887 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031724022 Printed edition: 9783031724046 Printed edition: 9783031724053 Springer Theses, Recognizing Outstanding Ph.D. Research, 2190-5061 66370 https://doi.org/10.1007/978-3-031-72403-9 ZDB-2-PHA ZDB-2-SXP 64446 64446