Discreteness corrections and higher spatial derivatives in effective canonical quantum gravity

Canonical quantum theories with discrete space may imply interesting effects. This paper presents a general effective description, paying due attention to the role of higher spatial derivatives in a local expansion and differences to higher time derivatives. In a concrete set of models, it is shown that spatial derivatives one order higher than the classical one are strongly restricted in spherically symmetric effective loop quantum gravity. Moreover, radial holonomy corrections alone cannot be anomaly free to this order.