  The general problem of representing the Greens function $G(k,z)$ in terms of
self energy, in field theories lacking Wick's theorem, is considered. A simple
construction shows that a Dyson like representation with a self energy
$\Sigma(k,z)$ is always possible, provided we start with a spectral
representation for $G(k,z)$ for finite sized systems and take the thermodynamic
limit. The self energy itself can then be iteratively expressed in terms of
another higher order self energy, capturing the spirit of Mori's formulation.
  We further discuss alternative and more general forms of $G(k,z)$ that are
possible. In particular, a recent theory by the author of extremely correlated
Fermi liquids at density "$n$", for Gutzwiller projected non canonical Fermi
operators obtains a new form of the Greens function: $$G(k,z)= \frac{\{1-
\frac{n}{2}\} + \Psi(k,z)}{z - \hat{E}_k - \Phi(k,z)}, $$ with {\em a pair of
self energies} $\Phi(z)$ and $\Psi(z)$. Its relationship with the Dyson form is
explored. A simple version of the two self energy model was shown recently to
successfully fit several data sets of photoemission line shapes in cuprates. We
provide details of the unusual spectral line shapes that arise in this model,
with the characteristic skewed shape depending upon a single parameter. The EDC
and MDC line shapes are shown to be skewed in opposite directions, and provide
a testable prediction of the theory.
