Relative entropy of single-mode squeezed states in Quantum Field Theory
Abstract Utilizing the Tomita–Takesaki modular theory, we derive a closed-form analytic expression for the Araki–Uhlmann relative entropy between a single-mode squeezed state and the vacuum state in a free relativistic massive scalar Quantum Field Theory within wedge regions of Minkowski spacetime....
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-06-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-025-14413-5 |
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| author | Marcelo S. Guimaraes Itzhak Roditi Silvio P. Sorella Arthur F. Vieira |
| author_facet | Marcelo S. Guimaraes Itzhak Roditi Silvio P. Sorella Arthur F. Vieira |
| author_sort | Marcelo S. Guimaraes |
| collection | DOAJ |
| description | Abstract Utilizing the Tomita–Takesaki modular theory, we derive a closed-form analytic expression for the Araki–Uhlmann relative entropy between a single-mode squeezed state and the vacuum state in a free relativistic massive scalar Quantum Field Theory within wedge regions of Minkowski spacetime. Similarly to the case of coherent states, this relative entropy is proportional to the smeared Pauli–Jordan distribution. Consequently, the Araki–Uhlmann entropy between a single-mode squeezed state and the vacuum satisfies all expected properties: it remains positive, increases with the size of the Minkowski region under consideration, and decreases as the mass parameter grows. |
| format | Article |
| id | doaj-art-9f74ceb4e2f74bcfa7815142b6cd974f |
| institution | Kabale University |
| issn | 1434-6052 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj-art-9f74ceb4e2f74bcfa7815142b6cd974f2025-08-20T03:37:40ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522025-06-018561810.1140/epjc/s10052-025-14413-5Relative entropy of single-mode squeezed states in Quantum Field TheoryMarcelo S. Guimaraes0Itzhak Roditi1Silvio P. Sorella2Arthur F. Vieira3Instituto de Física-Departamento de Física Teórica, UERJ-Universidade do Estado do Rio de JaneiroCBPF-Centro Brasileiro de Pesquisas FísicasInstituto de Física-Departamento de Física Teórica, UERJ-Universidade do Estado do Rio de JaneiroInstituto de Física-Departamento de Física Teórica, UERJ-Universidade do Estado do Rio de JaneiroAbstract Utilizing the Tomita–Takesaki modular theory, we derive a closed-form analytic expression for the Araki–Uhlmann relative entropy between a single-mode squeezed state and the vacuum state in a free relativistic massive scalar Quantum Field Theory within wedge regions of Minkowski spacetime. Similarly to the case of coherent states, this relative entropy is proportional to the smeared Pauli–Jordan distribution. Consequently, the Araki–Uhlmann entropy between a single-mode squeezed state and the vacuum satisfies all expected properties: it remains positive, increases with the size of the Minkowski region under consideration, and decreases as the mass parameter grows.https://doi.org/10.1140/epjc/s10052-025-14413-5 |
| spellingShingle | Marcelo S. Guimaraes Itzhak Roditi Silvio P. Sorella Arthur F. Vieira Relative entropy of single-mode squeezed states in Quantum Field Theory European Physical Journal C: Particles and Fields |
| title | Relative entropy of single-mode squeezed states in Quantum Field Theory |
| title_full | Relative entropy of single-mode squeezed states in Quantum Field Theory |
| title_fullStr | Relative entropy of single-mode squeezed states in Quantum Field Theory |
| title_full_unstemmed | Relative entropy of single-mode squeezed states in Quantum Field Theory |
| title_short | Relative entropy of single-mode squeezed states in Quantum Field Theory |
| title_sort | relative entropy of single mode squeezed states in quantum field theory |
| url | https://doi.org/10.1140/epjc/s10052-025-14413-5 |
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