  Spinfoam theories are hoped to provide the dynamics of non-perturbative loop
quantum gravity. But a number of their features remain elusive. The best
studied one -the euclidean Barrett-Crane model- does not have the boundary
state space needed for this, and there are recent indications that,
consequently, it may fail to yield the correct low-energy $n$-point functions.
These difficulties can be traced to the SO(4) -> SU(2) gauge fixing and the way
certain second class constraints are imposed, arguably incorrectly, strongly.
We present an alternative model, that can be derived as a bona fide
quantization of a Regge discretization of euclidean general relativity, and
where the constraints are imposed weakly. Its state space is a natural subspace
of the SO(4) spin-network space and matches the SO(3) hamiltonian spin network
space. The model provides a long sought SO(4)-covariant vertex amplitude for
loop quantum gravity.
