Quantum scalar field theories with fractional operators

We study a class of perturbative scalar quantum field theories where dynamics is characterized by Lorentz-invariant or Lorentz-breaking non-local operators of fractional order and the underlying spacetime has a varying spectral dimension. These theories are either ghost free or power-counting renormalizable but they cannot be both at the same time. However, some of them are one-loop unitary and finite, and possibly unitary and finite at all orders.

Automated summary

We studied a class of perturbative scalar quantum field theories characterized by specific operators; some of them are ghost free, some are power-counting renormalizable, but cannot be both; for some of these theories, one-loop calculations result in unitary and finite theories, potentially valid at all orders.