Quantum field theory of physical and purely virtual particles in a finite interval of time on a compact space manifold: diagrams, amplitudes and unitarity
Abstract We provide a diagrammatic formulation of perturbative quantum field theory in a finite interval of time τ, on a compact space manifold Ω. We explain how to compute the evolution operator U(t f , t i) between the initial time t i and the final time t f = t i + τ, study unitarity and renormal...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-07-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP07(2023)209 |
| _version_ | 1797647444588101632 |
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| author | Damiano Anselmi |
| author_facet | Damiano Anselmi |
| author_sort | Damiano Anselmi |
| collection | DOAJ |
| description | Abstract We provide a diagrammatic formulation of perturbative quantum field theory in a finite interval of time τ, on a compact space manifold Ω. We explain how to compute the evolution operator U(t f , t i) between the initial time t i and the final time t f = t i + τ, study unitarity and renormalizability, and show how to include purely virtual particles, by rendering some physical particles (and all the ghosts, if present) purely virtual. The details about the restriction to finite τ and compact Ω are moved away from the internal sectors of the diagrams (apart from the discretization of the three-momenta), and coded into external sources. Unitarity is studied by means of the spectral optical identities, and the diagrammatic version of the identity U †(t f , t i)U(t f , t i) = 1. The dimensional regularization is extended to finite τ and compact Ω, and used to prove, under general assumptions, that renormalizability holds whenever it holds at τ = ∞, Ω = ℝ3. Purely virtual particles are introduced by removing the on-shell contributions of some physical particles, and the ghosts, from the core diagrams, and trivializing their initial and final conditions. The resulting evolution operator U ph(t f , t i) is unitary, but does not satisfy the more general identity U ph(t 3 , t 2)U ph(t 2 , t 1) = U ph(t 3 , t 1). As a consequence, U ph(t f , t i) cannot be derived from a Hamiltonian in a standard way, in the presence of purely virtual particles. |
| first_indexed | 2024-03-11T15:17:28Z |
| format | Article |
| id | doaj.art-09e16d6d1be54c29a89bb66965563b57 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-11T15:17:28Z |
| publishDate | 2023-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-09e16d6d1be54c29a89bb66965563b572023-10-29T12:06:26ZengSpringerOpenJournal of High Energy Physics1029-84792023-07-012023715710.1007/JHEP07(2023)209Quantum field theory of physical and purely virtual particles in a finite interval of time on a compact space manifold: diagrams, amplitudes and unitarityDamiano Anselmi0Dipartimento di Fisica “E.Fermi”, Università di PisaAbstract We provide a diagrammatic formulation of perturbative quantum field theory in a finite interval of time τ, on a compact space manifold Ω. We explain how to compute the evolution operator U(t f , t i) between the initial time t i and the final time t f = t i + τ, study unitarity and renormalizability, and show how to include purely virtual particles, by rendering some physical particles (and all the ghosts, if present) purely virtual. The details about the restriction to finite τ and compact Ω are moved away from the internal sectors of the diagrams (apart from the discretization of the three-momenta), and coded into external sources. Unitarity is studied by means of the spectral optical identities, and the diagrammatic version of the identity U †(t f , t i)U(t f , t i) = 1. The dimensional regularization is extended to finite τ and compact Ω, and used to prove, under general assumptions, that renormalizability holds whenever it holds at τ = ∞, Ω = ℝ3. Purely virtual particles are introduced by removing the on-shell contributions of some physical particles, and the ghosts, from the core diagrams, and trivializing their initial and final conditions. The resulting evolution operator U ph(t f , t i) is unitary, but does not satisfy the more general identity U ph(t 3 , t 2)U ph(t 2 , t 1) = U ph(t 3 , t 1). As a consequence, U ph(t f , t i) cannot be derived from a Hamiltonian in a standard way, in the presence of purely virtual particles.https://doi.org/10.1007/JHEP07(2023)209Models of Quantum GravityNew Gauge InteractionsRenormalization and RegularizationScattering Amplitudes |
| spellingShingle | Damiano Anselmi Quantum field theory of physical and purely virtual particles in a finite interval of time on a compact space manifold: diagrams, amplitudes and unitarity Journal of High Energy Physics Models of Quantum Gravity New Gauge Interactions Renormalization and Regularization Scattering Amplitudes |
| title | Quantum field theory of physical and purely virtual particles in a finite interval of time on a compact space manifold: diagrams, amplitudes and unitarity |
| title_full | Quantum field theory of physical and purely virtual particles in a finite interval of time on a compact space manifold: diagrams, amplitudes and unitarity |
| title_fullStr | Quantum field theory of physical and purely virtual particles in a finite interval of time on a compact space manifold: diagrams, amplitudes and unitarity |
| title_full_unstemmed | Quantum field theory of physical and purely virtual particles in a finite interval of time on a compact space manifold: diagrams, amplitudes and unitarity |
| title_short | Quantum field theory of physical and purely virtual particles in a finite interval of time on a compact space manifold: diagrams, amplitudes and unitarity |
| title_sort | quantum field theory of physical and purely virtual particles in a finite interval of time on a compact space manifold diagrams amplitudes and unitarity |
| topic | Models of Quantum Gravity New Gauge Interactions Renormalization and Regularization Scattering Amplitudes |
| url | https://doi.org/10.1007/JHEP07(2023)209 |
| work_keys_str_mv | AT damianoanselmi quantumfieldtheoryofphysicalandpurelyvirtualparticlesinafiniteintervaloftimeonacompactspacemanifolddiagramsamplitudesandunitarity |