  We propose to describe the spin fluctuations in the normal state of
underdoped high $T_{c}$ superconductors as a manifestation of an algebraic spin
liquid. We have performed calculations within the slave-boson model to support
our proposal. Under the spin-charge separation picture, the normal state (the
spin-pseudogap phase) is described by massless Dirac fermions, charged bosons,
and a gauge field. We find that the gauge interaction is a marginal
perturbation and drives the mean-field free-spinon fixed point to a more
complicated spin-quantum-fixed-point -- the algebraic spin liquid, where
gapless excitations interact at low energies. The electron spectral function in
the normal state was found to have a Luttinger-liquid-like line shape as
observed in experiments. The spectral function obtained in the superconducting
state shows how a coherent quasiparticle peak appears from the incoherent
background as spin and charge recombine.
