Theory of extreme correlations using canonical Fermions and path integrals

The t-J model is studied using a novel and rigorous mapping of the Gutzwiller projected electrons, in terms of canonical electrons. The mapping has considerable similarity to the Dyson-Maleev transformation relating spin operators to canonical Bosons. This representation gives rise to a non Hermitean quantum theory, characterized by minimal redundancies. A path integral representation of the canonical theory is given. Using it, the salient results of the extremely correlated Fermi liquid (ECFL) theory, including the previously found Schwinger equations of motion, are easily rederived. Further a transparent physical interpretation of the previously introduced auxiliary Greens functions and the caparison factor is obtained. The low energy electron spectral function in this theory with a strong intrinsic asymmetry, is summarized in terms of a few expansion coefficients. These include an important emergent energy scale $Delta_0$ that shrinks to zero on approaching the insulating state, thereby making it difficult to access the underlying low energy Fermi liquid behavior. The scaled low frequency ECFL spectral function is related simply to the Fano line shape. The resulting energy dispersion (EDC or MDC) is a hybrid of a massive and a massless Dirac spectrum $ E^*_Qsim gamma, Q- sqrt{Gamma_0^2 + Q^2} $, where the vanishing of $Q$, a momentum like variable, locates the kink. Therefore the quasiparticle velocity interpolates between $(gamma mp 1)$ over a width $Gamma_0$ on the two sides of $Q=0$. The resulting kink strongly resembles a prominent low energy feature seen in angle resolved photoemission spectra (ARPES) of cuprate materials. We also propose novel ways of analyzing the ARPES data to isolate the predicted asymmetry between particle and hole excitations.