Vacuum and thermal fluctuations of a scalar field with point interactions
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911671749967872 |
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| author | Fermi, Davide Gurgoglione, Marco |
| author_facet | Fermi, Davide Gurgoglione, Marco |
| contents | We investigate the vacuum and thermal fluctuations of a neutral massless scalar field living in Minkowski spacetime and interacting with a finite number of point-like obstacles, modelled by zero-range potentials. The system is described rigorously in terms of self-adjoint realizations of the Laplacian, under assumptions ensuring the absence of instabilities. Using the relative zeta-function technique, we determine the renormalized connected partition function and derive explicit expressions for the thermodynamic observables, characterizing both their low- and high-temperature behaviours. Furthermore, we derive of a convergent Born series expansion for the Casimir energy, which identifies multiple-scattering processes as the mechanism underlying vacuum forces. The latter decompose into pairwise contributions directed along the lines joining the obstacles, with intensities depending non-locally on the full configuration. We also present some numerical results for identical obstacles, indicating that the Casimir forces are always attractive in this context. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_10725 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Vacuum and thermal fluctuations of a scalar field with point interactions Fermi, Davide Gurgoglione, Marco Mathematical Physics Mesoscale and Nanoscale Physics Quantum Physics 81T55, 81T20, 81T28, 81U15, 81Q10 We investigate the vacuum and thermal fluctuations of a neutral massless scalar field living in Minkowski spacetime and interacting with a finite number of point-like obstacles, modelled by zero-range potentials. The system is described rigorously in terms of self-adjoint realizations of the Laplacian, under assumptions ensuring the absence of instabilities. Using the relative zeta-function technique, we determine the renormalized connected partition function and derive explicit expressions for the thermodynamic observables, characterizing both their low- and high-temperature behaviours. Furthermore, we derive of a convergent Born series expansion for the Casimir energy, which identifies multiple-scattering processes as the mechanism underlying vacuum forces. The latter decompose into pairwise contributions directed along the lines joining the obstacles, with intensities depending non-locally on the full configuration. We also present some numerical results for identical obstacles, indicating that the Casimir forces are always attractive in this context. |
| title | Vacuum and thermal fluctuations of a scalar field with point interactions |
| topic | Mathematical Physics Mesoscale and Nanoscale Physics Quantum Physics 81T55, 81T20, 81T28, 81U15, 81Q10 |
| url | https://arxiv.org/abs/2605.10725 |