LQG formulations have a minimum length/area. Since say, a Planck area can always be boosted, any minimum area in space can be shrunk. Do LQG proponents worry about local Lorentz invariance violation, and if not, why not? In LQG, does considering length to be a quantum operator really get rid of the boost problem?
This has been asked and answered before: see Does the discreteness of spacetime in canonical approaches imply good bye to STR?
Also, this question has popped up many times on other sites such as physicsforums: http://www.physicsforums.com/showthread.php?t=281951
The answer is roughly that LQG does not in fact violate Lorentz invariance. The discretisation of area and volume operators does not imply a broken symmetry, any more than discretisation of angular momentum states imply breaking of rotational symmetry --- symmetries in quantum theories are equations of the operator algebra, not of the states!
See also: http://arxiv.org/abs/1012.1739