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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/2410.15300 |
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| _version_ | 1866929551589769216 |
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| author | Arjun, K. Vinodkumar, A M Bannur, Vishnu Mayya Mustafa, Munshi G. |
| author_facet | Arjun, K. Vinodkumar, A M Bannur, Vishnu Mayya Mustafa, Munshi G. |
| contents | The running coupling constant is calculated using the imaginary time formalism (ITF) of thermal field theory under the self-energy approximation. In the process, each Feynman diagram in thermal field theory is rewritten as the summation of non-thermal diagrams with coefficients that are functions of mass and temperature. By employing the same mass scale and coupling constant for both the non-thermal QFT and ITF, we derive a relation between them. Also, we calculate the self-energy using ITF, which is equated to the same as that of non-thermal QFT under the zero external momentum limit. This can provide a new expression for the coupling constant. Combining this result with the $β(g)$ and $γ_m(g)$ function relations of the renormalization group equations gives rise to a thermal-dependent coupling constant and running mass. Using these results, the free energy density is evaluated for two-loop order and compared with quasiparticle model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_15300 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Self-Energy Approximation for the Running Coupling Constant in Thermal $ϕ^4$ Theory using Imaginary Time Formalism Arjun, K. Vinodkumar, A M Bannur, Vishnu Mayya Mustafa, Munshi G. High Energy Physics - Theory The running coupling constant is calculated using the imaginary time formalism (ITF) of thermal field theory under the self-energy approximation. In the process, each Feynman diagram in thermal field theory is rewritten as the summation of non-thermal diagrams with coefficients that are functions of mass and temperature. By employing the same mass scale and coupling constant for both the non-thermal QFT and ITF, we derive a relation between them. Also, we calculate the self-energy using ITF, which is equated to the same as that of non-thermal QFT under the zero external momentum limit. This can provide a new expression for the coupling constant. Combining this result with the $β(g)$ and $γ_m(g)$ function relations of the renormalization group equations gives rise to a thermal-dependent coupling constant and running mass. Using these results, the free energy density is evaluated for two-loop order and compared with quasiparticle model. |
| title | Self-Energy Approximation for the Running Coupling Constant in Thermal $ϕ^4$ Theory using Imaginary Time Formalism |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2410.15300 |