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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| Accès en ligne: | https://arxiv.org/abs/2407.02707 |
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| _version_ | 1866916549191794688 |
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| author | Aggarwal, Ankit Barnich, Glenn |
| author_facet | Aggarwal, Ankit Barnich, Glenn |
| contents | We compute the exact thermal partition functions of a massive scalar field on flat spacetime backgrounds of the form $\mathbb R^{d-q}\times \mathbb T^{q+1}$ and show that they possess an ${\rm SL}(q+1,\mathbb Z)$ symmetry. Non-trivial relations between equivalent expressions for the result are obtained by doing the computation using functional, canonical and worldline methods. For $q=1$, the results exhibit modular symmetry and may be expressed in terms of massive Maass-Jacobi forms. In the complex case with chemical potential for ${\rm U}(1)$ charge turned on, the usual discussion of relativistic Bose-Einstein condensation is modified by the presence of the small dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_02707 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Modular properties of massive scalar partition functions Aggarwal, Ankit Barnich, Glenn High Energy Physics - Theory Statistical Mechanics We compute the exact thermal partition functions of a massive scalar field on flat spacetime backgrounds of the form $\mathbb R^{d-q}\times \mathbb T^{q+1}$ and show that they possess an ${\rm SL}(q+1,\mathbb Z)$ symmetry. Non-trivial relations between equivalent expressions for the result are obtained by doing the computation using functional, canonical and worldline methods. For $q=1$, the results exhibit modular symmetry and may be expressed in terms of massive Maass-Jacobi forms. In the complex case with chemical potential for ${\rm U}(1)$ charge turned on, the usual discussion of relativistic Bose-Einstein condensation is modified by the presence of the small dimensions. |
| title | Modular properties of massive scalar partition functions |
| topic | High Energy Physics - Theory Statistical Mechanics |
| url | https://arxiv.org/abs/2407.02707 |