Quantum scalar field theories with fractional operators
arXiv:2102.03363 · doi:10.1088/1361-6382/ac103c
Abstract
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.
arXiv comment49 pages, 5 figures. v2: gravity part moved into a separate paper (arXiv:2106.15430), advanced/retarded Green's functions added, unitarity proof with self-interactions added, connection with IR nonlocal gravity models strengthened, references added; v3: minor typos corrected, mistake corrected in equation (119) which propagated to some equations but did not alter any of the conclusions
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