Yang-Mills Field in the $κ$-space-time
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916869919735808 |
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| author | R, Bhagya. Harikumar, E. |
| author_facet | R, Bhagya. Harikumar, E. |
| contents | In this paper, we construct $SU(N)$ Yang-Mills theory in the $κ$-space-time, valid up to first order in the deformation parameter $a$, using the generalisation of Feynman's approach. Using the $κ$-deformed Wong's equation derived, in the Jacobi identity involving velocities and coordinates of $κ$-deformed space-time, the $κ$-deformed homogeneous Yang-Mills equations are derived. We show the compatibility between the $κ$-deformed field strength derived using the Jacobi identity and the commutators of the gauge covariant derivative, up to first order in $a$. The $κ$-deformed field strength is covariant under $SU(N)$ gauge transformations. We then construct the Lagrangian for Yang-Mills theory in $κ$-deformed space-time and show that it is invariant under $SU(N)$ transformation and not under U(N) transformation. We also derive the expression for the force experienced by an isospin-carrying particle in the presence of Yang-Mills field in the $κ$-space-time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_11501 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Yang-Mills Field in the $κ$-space-time R, Bhagya. Harikumar, E. High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Phenomenology In this paper, we construct $SU(N)$ Yang-Mills theory in the $κ$-space-time, valid up to first order in the deformation parameter $a$, using the generalisation of Feynman's approach. Using the $κ$-deformed Wong's equation derived, in the Jacobi identity involving velocities and coordinates of $κ$-deformed space-time, the $κ$-deformed homogeneous Yang-Mills equations are derived. We show the compatibility between the $κ$-deformed field strength derived using the Jacobi identity and the commutators of the gauge covariant derivative, up to first order in $a$. The $κ$-deformed field strength is covariant under $SU(N)$ gauge transformations. We then construct the Lagrangian for Yang-Mills theory in $κ$-deformed space-time and show that it is invariant under $SU(N)$ transformation and not under U(N) transformation. We also derive the expression for the force experienced by an isospin-carrying particle in the presence of Yang-Mills field in the $κ$-space-time. |
| title | Yang-Mills Field in the $κ$-space-time |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2411.11501 |