# Extremely Correlated Quantum Liquids

## TL;DR

This paper develops a theoretical framework for extremely correlated electron liquids, extending Fermi liquid theory, and introduces novel equations and transformations to analyze their unique physical properties.

## Contribution

It generalizes Fermi liquid theory to strongly correlated systems using Schwinger source fields and matrix scale transformations, providing a new formalism for such quantum liquids.

## Key findings

- Derived an exact Dyson equation for quasiparticle Green's functions.
- Established Ward identities for systematic approximations.
- Presented preliminary calculations demonstrating the formalism's application.

## Abstract

We formulate the theory of an extremely correlated electron liquid, generalizing the standard Fermi liquid. This quantum liquid has specific signatures in various physical properties, such as the Fermi surface volume and the narrowing of electronic bands by spin and density correlation functions. We use Schwinger's source field idea to generate equations for the Greens function for the Hubbard operators. A local (matrix) scale transformation in the time domain to a quasiparticle Greens function, is found to be optimal. This transformation allows us to generate vertex functions that are guaranteed to reduce to the bare values for high frequencies, i.e. are ``asymptotically free''. The quasiparticles are fractionally charged objects, and we find an exact Schwinger Dyson equation for their Greens function. We find a hierarchy of equations for the vertex functions, and further we obtain Ward identities so that systematic approximations are feasible. An expansion in terms of the density of holes measured from the Mott Hubbard insulating state follows from the nature of the theory. A systematic presentation of the formalism is followed by some preliminary explicit calculations.