  A new framework of loop quantization that assimilates conformal and scale
invariance is constructed and is found to be applicable to a large class of
physically important theories of gravity and gravity-matter systems. They
include general relativity and scale-invariant scalar-tensor and dilaton
theories. Consequently, matter to be coupled to such theories is restricted to
be conformal or scale invariant. Standard model-type systems naturally fall
into this category. The new loop quantization follows from a novel conformally
generalized Holst action principle. In contrast to standard loop quantum
gravity, the resulting quantum geometry is not beset by the Immirzi ambiguity
and has no definitive area gaps within the considered large class of theories
of gravitation. As an additional feature, the scale invariance gives rise to a
conserved Weyl current and we discuss briefly its possible implication on the
problem of time in quantum gravity.
