Aspects of non-perturbative unitarity in Quantum Field Theory

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According to the Asymptotic Safety conjecture, a (non-perturbatively)
renormalizable quantum field theory of gravity could be constructed
based on the existence of a non-trivial fixed point of the
renormalization group flow.
The existence of this fixed point can be established, e.g., via the
non-perturbative methods of the functional renormalization group (FRG).
In practice, the use of the FRG methods requires to work within
truncations of the gravitational action, and higher-derivative operators
naturally lead to the presence of several poles in the propagator. The
question is whether these poles represent a real problem for the
unitarity of the theory.

Using QED as a working example, in this talk I will discuss some aspects
of non-perturbative unitarity in Quantum Field Theory. I will show that
the inclusion of quantum effects at all scales is of crucial importance
to assess unitarity of field theories. In particular, poles appearing in
truncations of the action could correspond to fake degrees of freedom of
the theory. Possible conditions to determine, within truncations,
whether a pole represents a fake or a genuine degree of freedom of the
theory will also be discussed.