# Abstract:

We construct the low energy theory of a doped Mott insulator, such as
the high-temperature superconductors, by explicitly integrating over the

degrees of freedom far away from the chemical potential. For either hole
or electron doping, a
charge 2e bosonic field emerges at low energy. The charge 2e boson mediates
dynamical spectral weight transfer
across the Mott gap and creates a new charge
*
e
*
excitation by binding a
hole. The result is a bifurcation
of the electron dispersion below the chemical potential as observed
recently in angle-resolved photoemission on Pb-doped

Bi
_{
2
}
Sr
_{
2
}
CaCu
_{
2
}
O
_{
8+\delta
}
(Pb2212). In addition, we show
that the 1) mid-infrared band in the optical conductivity, 2) the

T
^{
2
}
contribution to the thermal conductivity, 3) the pseudogap,
4)insulating behaviour away from half-filling, 5) the high and

low-energy kinks in the electron dispersion and 6) T-linear
resistivity all derive from the charge 2e boson.

1.) R. G. Leigh, P. Phillips, and T. -P. Choy,

Phys. Rev. Lett. vol. 99, 46404 (2007).

2.) T. -P. Choy, R. G. Leigh, P. Phillips, and P. D. Powell, PRB, in

press (arXiv:0707.1554); arXiv: ibid, 0712.2841.