Postmodern Fermi Liquids: A Conceptual Overview

Umang Mehta

Joel Feldman, Horst Kn�rrer, Eugene Trubowitz B

Umang Mehta

We develop, in this dissertation, a theoretical formalism for Fermi liquids by exploiting an underlying algebro-geometric 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 thereby allows us to write down a nonlinear, bosonized action that reproduces Landau's kinetic theory in the classical limit. Upon quantizing, we obtain a systematic effective field theory as an expansion in nonlinear and higher derivative corrections suppressed by the Fermi momentum pF , without the need to introduce artificial momentum scales through, e.g., decomposition of the Fermi surface into patches. We find 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. We survey the benefits and limitations of this geometric formalism in the context of scaling, diagrammatic calcu- lations, scattering and interactions, coupling to background gauge fields, etc. After setting up a path to extending this formalism to include superconducting and magnetic phases, as well as applications to the problem of non-Fermi liquids, we conclude with a discussion on possible future directions for Fermi surface physics, and more broadly, the usefulness of diffeomorphism groups in condensed matter physics.

D. ter Haar

Gordon G. Globus

I “think together” quantum brain dynamics (QBD) and postmodernism (appropriated to include Heidegger). In particular, the world thrownness of Heidegger, the sovereignty of Bataille and the differance of Derrida can be talked about in terms of QBD. This effects a rapprochement between the QBD revolution against classical neural network brain theory and the postmodern revolution against modernity and the metaphysical tradition. Such a grand millenial rapprochement brings together science in the guise of quantum neurophysics and postmodernism against their respective wills. Discussion of the problem of “consciousness” and brain has been so stalemated and seemingly interminable that if progress is to be made, a great conceptual wrenching is only to be expected. My formulation relinquishes consciousness and the quotidian world-in-common in favor of existence and parallel world-thrownnesses.