Symplectic quantization and general constraint structure of a prototypical second-class system
Abstract We discuss a general prototypical constrained Hamiltonian system with a broad application in quantum field theory and similar contexts where dynamics is defined through a functional action obeying a stationarity principle. The prototypical model amounts to a Dirac–Bergmann singular system,...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-12-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-024-13631-7 |
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| author | Ignacio S. Gomez Vipul Kumar Pandey Ronaldo Thibes |
| author_facet | Ignacio S. Gomez Vipul Kumar Pandey Ronaldo Thibes |
| author_sort | Ignacio S. Gomez |
| collection | DOAJ |
| description | Abstract We discuss a general prototypical constrained Hamiltonian system with a broad application in quantum field theory and similar contexts where dynamics is defined through a functional action obeying a stationarity principle. The prototypical model amounts to a Dirac–Bergmann singular system, whose constraints restrict the actual dynamics to occur within a differential submanifold, as is the case in the major part of field theoretical models with gauge symmetry. We apply the Dirac–Bergmann algorithm in its full generality unraveling a total of 4m second-class constraints and obtain the corresponding Dirac brackets algebra in phase space. We follow with the Faddeev–Jackiw–Barcelos–Wotzasek approach in which the geometric character of the mentioned submanifold is emphasized by means of an internal metric function encoding its symplectic properties. We consider two straightforward examples, applying our general results to constrained motion along a toroidal geometry and to a Lorentz violating toy model in field theory. Since toroidal geometry has been recently used in cosmological models, we suggest how our results could lead to different proposals for the shape of the universe in cosmology. |
| format | Article |
| id | doaj-art-091c33c9fb7542ecb73b0330631bae80 |
| institution | Kabale University |
| issn | 1434-6052 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj-art-091c33c9fb7542ecb73b0330631bae802025-02-02T12:39:32ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522024-12-0184121910.1140/epjc/s10052-024-13631-7Symplectic quantization and general constraint structure of a prototypical second-class systemIgnacio S. Gomez0Vipul Kumar Pandey1Ronaldo Thibes2Universidade Estadual do Sudoeste da BahiaDepartment of Physics, Chandigarh UniversityUniversidade Estadual do Sudoeste da BahiaAbstract We discuss a general prototypical constrained Hamiltonian system with a broad application in quantum field theory and similar contexts where dynamics is defined through a functional action obeying a stationarity principle. The prototypical model amounts to a Dirac–Bergmann singular system, whose constraints restrict the actual dynamics to occur within a differential submanifold, as is the case in the major part of field theoretical models with gauge symmetry. We apply the Dirac–Bergmann algorithm in its full generality unraveling a total of 4m second-class constraints and obtain the corresponding Dirac brackets algebra in phase space. We follow with the Faddeev–Jackiw–Barcelos–Wotzasek approach in which the geometric character of the mentioned submanifold is emphasized by means of an internal metric function encoding its symplectic properties. We consider two straightforward examples, applying our general results to constrained motion along a toroidal geometry and to a Lorentz violating toy model in field theory. Since toroidal geometry has been recently used in cosmological models, we suggest how our results could lead to different proposals for the shape of the universe in cosmology.https://doi.org/10.1140/epjc/s10052-024-13631-7 |
| spellingShingle | Ignacio S. Gomez Vipul Kumar Pandey Ronaldo Thibes Symplectic quantization and general constraint structure of a prototypical second-class system European Physical Journal C: Particles and Fields |
| title | Symplectic quantization and general constraint structure of a prototypical second-class system |
| title_full | Symplectic quantization and general constraint structure of a prototypical second-class system |
| title_fullStr | Symplectic quantization and general constraint structure of a prototypical second-class system |
| title_full_unstemmed | Symplectic quantization and general constraint structure of a prototypical second-class system |
| title_short | Symplectic quantization and general constraint structure of a prototypical second-class system |
| title_sort | symplectic quantization and general constraint structure of a prototypical second class system |
| url | https://doi.org/10.1140/epjc/s10052-024-13631-7 |
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