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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.02633 |
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| _version_ | 1866929613511327744 |
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| author | García, J. Antonio Cruz-Alvarez, Rafael |
| author_facet | García, J. Antonio Cruz-Alvarez, Rafael |
| contents | A relation between the Dirac bracket (DB) and Nambu bracket (NB) is presented. The Nambu bracket can be related with Dirac bracket if we can write the DB as a generalized Poisson structure. The NB associated with DB have all the standard properties of the original DB. When the dimension of the phase space is $s+2$ where $s$ is the number of second class constraints, the associated Nambu structure has $s+2$ entries and reduces to the Dirac bracket when $s$ of its entries are fixed to be the second class constraints. In general, when the dimension of phase space is $d=r+s$ a new Nambu structure that describes correctly the constrained dynamics can also be constructed but in thsi case addicional conditidionts are requiered. In that case the associated NB corresponds to a ``Dirac-Nambu'' bracket with $r$ entries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_02633 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dirac bracket and Nambu structures García, J. Antonio Cruz-Alvarez, Rafael High Energy Physics - Theory Mathematical Physics A relation between the Dirac bracket (DB) and Nambu bracket (NB) is presented. The Nambu bracket can be related with Dirac bracket if we can write the DB as a generalized Poisson structure. The NB associated with DB have all the standard properties of the original DB. When the dimension of the phase space is $s+2$ where $s$ is the number of second class constraints, the associated Nambu structure has $s+2$ entries and reduces to the Dirac bracket when $s$ of its entries are fixed to be the second class constraints. In general, when the dimension of phase space is $d=r+s$ a new Nambu structure that describes correctly the constrained dynamics can also be constructed but in thsi case addicional conditidionts are requiered. In that case the associated NB corresponds to a ``Dirac-Nambu'' bracket with $r$ entries. |
| title | Dirac bracket and Nambu structures |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2412.02633 |