  In this work, we study the classical and quantum properties of the unique
commutative Lorentz-covariant connection for loop quantum gravity. This
connection has been found after solving the second-class constraints inherited
from the canonical analysis of the Holst action without the time-gauge. We show
that it has the property of lying in the conjugacy class of a pure $\su(2)$
connection, a result which enables one to construct the kinematical Hilbert
space of the Lorentz-covariant theory in terms of the usual $\SU(2)$
spin-network states. Furthermore, we show that there is a unique
Lorentz-covariant electric field, up to trivial and natural equivalence
relations. The Lorentz-covariant electric field transforms under the adjoint
action of the Lorentz group, and the associated Casimir operators are shown to
be proportional to the area density. This gives a very interesting algebraic
interpretation of the area. Finally, we show that the action of the surface
operator on the Lorentz-covariant holonomies reproduces exactly the usual
discrete $\SU(2)$ spectrum of time-gauge loop quantum gravity. In other words,
the use of the time-gauge does not introduce anomalies in the quantum theory.
