Non-unitarity of Minkowskian non-local quantum field theories

Non-unitarity of Minkowskian non-local quantum field theories

Abstract 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 co...

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Main Authors: Fabio Briscese, Leonardo Modesto
Format: Article
Language:English
Published: SpringerOpen 2021-08-01
Series:European Physical Journal C: Particles and Fields
Online Access:https://doi.org/10.1140/epjc/s10052-021-09525-7
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spelling doaj-830602164a9346338745fe060f4fa3412021-08-15T11:14:19ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60441434-60522021-08-018181910.1140/epjc/s10052-021-09525-7Non-unitarity of Minkowskian non-local quantum field theoriesFabio Briscese0Leonardo Modesto1INdAM, Città UniversitariaDepartment of Physics, Southern University of Science and TechnologyAbstract 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.https://doi.org/10.1140/epjc/s10052-021-09525-7
collection DOAJ
language English
format Article
sources DOAJ
author Fabio Briscese
Leonardo Modesto
spellingShingle Fabio Briscese
Leonardo Modesto
Non-unitarity of Minkowskian non-local quantum field theories
European Physical Journal C: Particles and Fields
author_facet Fabio Briscese
Leonardo Modesto
author_sort Fabio Briscese
title Non-unitarity of Minkowskian non-local quantum field theories
title_short Non-unitarity of Minkowskian non-local quantum field theories
title_full Non-unitarity of Minkowskian non-local quantum field theories
title_fullStr Non-unitarity of Minkowskian non-local quantum field theories
title_full_unstemmed Non-unitarity of Minkowskian non-local quantum field theories
title_sort non-unitarity of minkowskian non-local quantum field theories
publisher SpringerOpen
series European Physical Journal C: Particles and Fields
issn 1434-6044
1434-6052
publishDate 2021-08-01
description Abstract 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.
url https://doi.org/10.1140/epjc/s10052-021-09525-7
work_keys_str_mv AT fabiobriscese nonunitarityofminkowskiannonlocalquantumfieldtheories
AT leonardomodesto nonunitarityofminkowskiannonlocalquantumfieldtheories
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