Gauge Invariance and Spinon-Dopon Confinement in the t-J Model: implications for Fermi Surface Reconstruction in the Cuprates

We discuss the application of the two-band spin-dopon representation of the t-J model to address the issue of the Fermi surface reconstruction observed in the cuprates. We show that the electron no double occupancy (NDO) constraint plays a key role in this formulation. In particular, the auxiliary lattice spin and itinerant dopon degrees of freedom of the spin-dopon formulation of the t-J model are shown to be confined in the emergent U(1) gauge theory generated by the NDO constraint. This constraint is enforced by the requirement of an infinitely large spin-dopon coupling. As a result, the t-J model is equivalent to a Kondo-Heisenberg lattice model of itinerant dopons and localized lattice spins at infinite Kondo coupling at all dopings. We show that mean-field treatment of the large vs small Fermi surface crossing in the cuprates which leaves out the NDO constraint, leads to inconsistencies and it is automatically excluded form the t - J model framework

On the stability of compact supermassive objects

Proceeded from the gravitation equations proposed by one of authors it was argued in a previous paper that there can exist supermassive compact configurations of degenerated Fermi-gas without events horizon. In the present paper we consider the stability of these objects by method like the one used in the theory of stellar structure. It is shown that the configurations with an adiabatic equation of state with the power 4/3 are stable.Comment: 10 pages, 5 figure