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The t-J model is studied using a novel and rigorous mapping of the Gutzwillerprojected electrons, in terms of canonical electrons. The mapping hasconsiderable similarity to the Dyson-Maleev transformation relating spinoperators to canonical Bosons. This representation gives rise to a nonHermitean quantum theory, characterized by minimal redundancies. A pathintegral representation of the canonical theory is given. Using it, the salientresults of the extremely correlated Fermi liquid (ECFL) theory, including thepreviously found Schwinger equations of motion, are easily rederived. Further atransparent physical interpretation of the previously introduced auxiliaryGreens functions and the caparison factor is obtained.  The low energy electron spectral function in this theory with a strongintrinsic asymmetry, is summarized in terms of a few expansion coefficients.These include an important emergent energy scale $\Delta_0$ that shrinks tozero on approaching the insulating state, thereby making it difficult to accessthe underlying low energy Fermi liquid behavior. The scaled low frequency ECFLspectral function is related simply to the Fano line shape. The resultingenergy dispersion (EDC or MDC) is a hybrid of a massive and a massless Diracspectrum $ E^*_Q\sim \gamma\, Q- \sqrt{\Gamma_0^2 + Q^2} $, where the vanishingof $Q$, a momentum like variable, locates the kink. Therefore the quasiparticlevelocity interpolates between $(\gamma \mp 1)$ over a width $\Gamma_0$ on thetwo sides of $Q=0$. The resulting kink strongly resembles a prominent lowenergy feature seen in angle resolved photoemission spectra (ARPES) of cupratematerials. We also propose novel ways of analyzing the ARPES data to isolatethe predicted asymmetry between particle and hole excitations.

Theory of extreme correlations using canonical Fermions and path integrals