Journal
EUROPEAN PHYSICAL JOURNAL C
Volume 81, Issue 8, Pages -Publisher
SPRINGER
DOI: 10.1140/epjc/s10052-021-09525-7
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We demonstrate that Minkowskian non-local quantum field theories are not unitary, as opposed to the case of Euclidean non-local scalar field which satisfies the Cutkosky rules. The breaking of unitarity in Minkowskian theory is clearly identified.
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.
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