2022/01/06 by Ganjitabar, Hassan
#FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2201.02201
Anisotropic Special Relativity (ASR) is the relativistic theory of nature with a preferred direction in space-time. By relaxing the full-isotropy constraint on space-time to the preference of one direction, we obtain a perturbative modification of the Minkowski metric as \mathscrgμν≃ημν+2ϕεμν 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 gμν. The mass of a the particle is modified to m2=Pμ\mathscrgμνPν which, in the first approximation level, has the extra term (2ϕεμν)PμPν 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 \mathscrgμν 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.