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The problem of time is one of the most relevant open issues in canonicalquantum gravity. Although there is a huge literature about this topic, acommonly accepted solution has not been found yet. Here, we focus on thesemiclassical approach to the problem of time, that has the main goal ofreproducing quantum field theory on a fixed WKB background accounting also forquantum gravity corrections. We analyze the different choices of the expansionparameter and discuss the problems arising in previous proposals, where anon-unitary evolution emerges as an effect of quantum gravity corrections. Inthis work we develop a new approach to solve this problem by performing the WKBexpansion with the introduction of the so-called kinematical action as a clockfor quantum matter, that allows to recover a unitary dynamics.

Non-Unitarity Problem in Quantum Gravity Corrections to Quantum Field Theory with Born-Oppenheimer Approximation