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| Format: | Preprint |
| Publié: |
2022
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2201.02201 |
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- Anisotropic Special Relativity (ASR) is the relativistic theory of nature with a preferred direction in space-time. By relaxing the \textit{full-isotropy} constraint on space-time to the \textit{preference of one direction}, we obtain a perturbative modification of the Minkowski metric as $\mathscr{g}_{μν}\simeqη_{μν}+2ϕε_{μν}$ for a small perturbation parameter $ϕ$. The symmetry group of ASR is obtained to have six generators satisfying the full Lorentz group algebra. However, the generators are deformed by the perturbation parameter $ϕ$. So, ASR retains the same representations of Special Relativity (SR) but allows for Lorentz-invariant violation at the same time. Any invariant quantity of the theory is the inner product of two contravariant 4-vectors mediated by ${g}_{μν}$. The mass of a the particle is modified to $m^2=P^μ\mathscr{g}_{μν}P^ν$ which, in the first approximation level, has the extra term $(2ϕε_{μν})P^μP^ν$ compared to the mass of the particle in SR. So, one application of ASR is, for example, to explain the neutrino flavour oscillation experiments in a natural way without violating the lepton number or adding sterile right-handed neutrinos. The mass of a particle is not the only quantity that is modified in ASR; any scalar quantity such as the Lagrangian of fields are also modified since the anisotropic metric $\mathscr{g}_{μν}$ is used to contract any pair of covariant-contravariant indices. As a more general consequence of ASR, any Quantum Field Theory (QFT) becomes anisotropic since the Lagrangian must contain the anisotropic metric. So, we provide a procedure to make anisotropic QFTs where the Lorentz-invariant Lagrangians are replaced with their ASR version.