  In a recent article [Science 317, 1705 (2007)], Anderson pointed out that
many theories about electron pairing in cuprate superconductors may be on the
wrong track and there is no reason to believe that the dynamic screening
(k-space) can provide a valid glue to hold the electron pairs together. On the
other hand, the most recent experimental observations imply the possible
generic existence of the real space localized Cooper pairs in amorphous
insulating and other nonsuperconducting systems [M. D. Stewart Jr. et al.,
Science 318, 1273 (2007)]. It is therefore clear that the glue for high-T_{c}
superconductors is relevant to the real space correlations. In this paper, we
argue that real space electron-electron interactions can play the role of glue
in high-T_{c} superconductors. It is found that two localized electrons, due to
a real space Coulomb confinement effect, can be in pairing inside a single
plaquette of the CuO plane. The scenario suggests appearance of a dominating
d-wave-like pairing symmetry in the hole-doped cuprates, while a more complex
mixed (s+d) symmetry in the electron-doped cuprates. Based on the mechanism,
the relationships between the superconductivity and the charge-stripe order are
discussed. In the La_{2-x}Sr_{x}CuO_{4} (LSCO) with 1/18\leq x\leq 1/4, we show
that the paired electrons can self-organize into the dimerized Wigner crystal.
Two kinds of quasi-one-dimensional metallic magnetic-charge stripes, where the
superconductivity and dynamical spin density wave (SDW) coexist, are
analytically determined. Furthermore, the physical original of the magic doping
fractions (at x=1/4, 1/8, 1/9, 1/16 and 1/18) of superconductivity and an
analytical phase diagram for LSCO are given.
