Diagrammar of physical and fake particles and spectral optical theorem

Abstract We prove spectral optical identities in quantum field theories of physical particles (defined by the Feynman iϵ prescription) and purely virtual particles (defined by the fakeon prescription). The identities are derived by means of purely algebraic operations and hold for every (multi)thres...

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Autor principal:	Damiano Anselmi
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2021
Materias:	Beyond Standard Model Models of Quantum Gravity Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
Acceso en línea:	https://doaj.org/article/bf39253762d94252a0d3e5cc9805af6a
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spelling	oai:doaj.org-article:bf39253762d94252a0d3e5cc9805af6a2021-11-08T11:16:34ZDiagrammar of physical and fake particles and spectral optical theorem10.1007/JHEP11(2021)0301029-8479https://doaj.org/article/bf39253762d94252a0d3e5cc9805af6a2021-11-01T00:00:00Zhttps://doi.org/10.1007/JHEP11(2021)030https://doaj.org/toc/1029-8479Abstract We prove spectral optical identities in quantum field theories of physical particles (defined by the Feynman iϵ prescription) and purely virtual particles (defined by the fakeon prescription). The identities are derived by means of purely algebraic operations and hold for every (multi)threshold separately and for arbitrary frequencies. Their major significance is that they offer a deeper understanding on the problem of unitarity in quantum field theory. In particular, they apply to “skeleton” diagrams, before integrating on the space components of the loop momenta and the phase spaces. In turn, the skeleton diagrams obey a spectral optical theorem, which gives the usual optical theorem for amplitudes, once the integrals on the space components of the loop momenta and the phase spaces are restored. The fakeon prescription/projection is implemented by dropping the thresholds that involve fakeon frequencies. We give examples at one loop (bubble, triangle, box, pentagon and hexagon), two loops (triangle with “diagonal”, box with diagonal) and arbitrarily many loops. We also derive formulas for the loop integrals with fakeons and relate them to the known formulas for the loop integrals with physical particles.Damiano AnselmiSpringerOpenarticleBeyond Standard ModelModels of Quantum GravityNuclear and particle physics. Atomic energy. RadioactivityQC770-798ENJournal of High Energy Physics, Vol 2021, Iss 11, Pp 1-40 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Beyond Standard Model Models of Quantum Gravity Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
spellingShingle	Beyond Standard Model Models of Quantum Gravity Nuclear and particle physics. Atomic energy. Radioactivity QC770-798 Damiano Anselmi Diagrammar of physical and fake particles and spectral optical theorem
description	Abstract We prove spectral optical identities in quantum field theories of physical particles (defined by the Feynman iϵ prescription) and purely virtual particles (defined by the fakeon prescription). The identities are derived by means of purely algebraic operations and hold for every (multi)threshold separately and for arbitrary frequencies. Their major significance is that they offer a deeper understanding on the problem of unitarity in quantum field theory. In particular, they apply to “skeleton” diagrams, before integrating on the space components of the loop momenta and the phase spaces. In turn, the skeleton diagrams obey a spectral optical theorem, which gives the usual optical theorem for amplitudes, once the integrals on the space components of the loop momenta and the phase spaces are restored. The fakeon prescription/projection is implemented by dropping the thresholds that involve fakeon frequencies. We give examples at one loop (bubble, triangle, box, pentagon and hexagon), two loops (triangle with “diagonal”, box with diagonal) and arbitrarily many loops. We also derive formulas for the loop integrals with fakeons and relate them to the known formulas for the loop integrals with physical particles.
format	article
author	Damiano Anselmi
author_facet	Damiano Anselmi
author_sort	Damiano Anselmi
title	Diagrammar of physical and fake particles and spectral optical theorem
title_short	Diagrammar of physical and fake particles and spectral optical theorem
title_full	Diagrammar of physical and fake particles and spectral optical theorem
title_fullStr	Diagrammar of physical and fake particles and spectral optical theorem
title_full_unstemmed	Diagrammar of physical and fake particles and spectral optical theorem
title_sort	diagrammar of physical and fake particles and spectral optical theorem
publisher	SpringerOpen
publishDate	2021
url	https://doaj.org/article/bf39253762d94252a0d3e5cc9805af6a
work_keys_str_mv	AT damianoanselmi diagrammarofphysicalandfakeparticlesandspectralopticaltheorem
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Diagrammar of physical and fake particles and spectral optical theorem

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