Delving into the Phenomenology of Very Special Relativity: From Subatomic Particles to Binary Stars
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arXiv
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| Format: | Preprint |
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2024
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| author | Santoni, Alessandro |
| author_facet | Santoni, Alessandro |
| contents | In this thesis, we investigate the implications of Lorentz-violating (LV) theories, focusing on Very Special Relativity (VSR) and its phenomenological consequences. Initially presented as an alternative mechanism for neutrino masses, VSR has since become a significant part of the general LV framework, distinguished by its unique group structure and non-local operators. After a comprehensive introduction to the principles of LV and VSR, we present the corresponding modifications to the Dirac equation. A significant part of the thesis is dedicated to the development of a Hamiltonian formalism within the VSR context, addressing its inherent non-localities. This approach is further extended to the non-relativistic limit, connecting it to the conventional Schrödinger picture. We then set upper bounds on the VSR parameters by examining its corrections to a wide range of physical systems and scenarios, such as Landau levels of charged particles, the $\mathsf g-$factor of electrons, the energy spectrum of ultracold neutrons in Earth's gravitational field, and the gravitational emission from binary stars. The latter analysis led us to the construction of a VSR field theory for spin-2 fields in flat space, which was surprisingly found to accommodate a gauge-invariant graviton mass. Through this comprehensive study, we bridged theoretical predictions with experimental data, paving the way for future explorations in Lorentz-violating theories and highlighting their potential to address unresolved questions in modern physics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_03104 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Delving into the Phenomenology of Very Special Relativity: From Subatomic Particles to Binary Stars Santoni, Alessandro High Energy Physics - Phenomenology General Relativity and Quantum Cosmology High Energy Physics - Theory In this thesis, we investigate the implications of Lorentz-violating (LV) theories, focusing on Very Special Relativity (VSR) and its phenomenological consequences. Initially presented as an alternative mechanism for neutrino masses, VSR has since become a significant part of the general LV framework, distinguished by its unique group structure and non-local operators. After a comprehensive introduction to the principles of LV and VSR, we present the corresponding modifications to the Dirac equation. A significant part of the thesis is dedicated to the development of a Hamiltonian formalism within the VSR context, addressing its inherent non-localities. This approach is further extended to the non-relativistic limit, connecting it to the conventional Schrödinger picture. We then set upper bounds on the VSR parameters by examining its corrections to a wide range of physical systems and scenarios, such as Landau levels of charged particles, the $\mathsf g-$factor of electrons, the energy spectrum of ultracold neutrons in Earth's gravitational field, and the gravitational emission from binary stars. The latter analysis led us to the construction of a VSR field theory for spin-2 fields in flat space, which was surprisingly found to accommodate a gauge-invariant graviton mass. Through this comprehensive study, we bridged theoretical predictions with experimental data, paving the way for future explorations in Lorentz-violating theories and highlighting their potential to address unresolved questions in modern physics. |
| title | Delving into the Phenomenology of Very Special Relativity: From Subatomic Particles to Binary Stars |
| topic | High Energy Physics - Phenomenology General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2409.03104 |