https://doi.org/10.1140/epjc/s10052-021-09525-7
Regular Article - Theoretical Physics
Non-unitarity of Minkowskian non-local quantum field theories
1
INdAM, Città Universitaria, P.le A. Moro 5, 00185, Rome, Italy
2
Department of Physics, Southern University of Science and Technology, 518055, Shenzhen, China
Received:
4
June
2021
Accepted:
4
August
2021
Published online:
14
August
2021
We show that Minkowskian non-local quantum field theories are not unitary. We consider a simple one loop diagram for a scalar non-local field and show that the imaginary part of the corresponding complex amplitude is not given by Cutkosky rules, indeed this diagram violates the unitarity condition. We compare this result with the case of an Euclidean non-local scalar field, that has been shown to satisfy the Cutkosky rules, and we clearly identify the reason of the breaking of unitarity of the Minkowskian theory.
© The Author(s) 2021
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