Extremely Correlated Fermi Liquids

We present the theory of an extremely correlated Fermi liquid with U -> infinity. This liquid has an underlying auxiliary Fermi liquid Green's function that is further caparisoned by extreme correlations. The theory leads to two parallel hierarchies of equations that permit iterative approximations in a certain parameter. Preliminary results for the spectral functions display a broad background and a distinct T dependent left skew. An important energy scale Delta((k) over right arrow, x) emerges as the average inelasticity of the FL Green's function, and influences the photoemission spectra profoundly. A duality is identified wherein a loss of coherence of the ECFL results from an excessively sharp FL.