The Marginal Fermi Liquid-A Derivation Based on Dirac's Constraints

Dirac's method for constraints is used for enforcing the exclusion of double occupancy for Correlated Electrons. The constraintt is given by the pair $Q(\vec{x})=\psi_{\downarrow}(\vec{x})\psi_{\uparrow}(\vec{x})$ which annihilates the ground state $|\Psi>$. Away from half fillings $Q(\vec{x})$ is replaced by a set of $first$ $class$ class Non-Abelian constraints $Q^{(-)}_{\alpha}(\vec{x})$ which are restricted to negative energies. The propagator for the single hole is determined by a measure which is a function of time duration for the hole propagator. a)-The imaginary part of the self energy - is linear in the frequency. b)-In the Superconducting phase the tunneling density of states is asymmetric.