Lorentz covariance

Summary

In relativistic physics, Lorentz symmetry or Lorentz invariance, named after the Dutch physicist Hendrik Lorentz, is an equivalence of observation or observational symmetry due to special relativity implying that the laws of physics stay the same for all observers that are moving with respect to one another within an inertial frame. It has also been described as "the feature of nature that says experimental results are independent of the orientation or the boost velocity of the laboratory through space". Lorentz covariance, a related concept, is a property of the underlying spacetime manifold. Lorentz covariance has two distinct, but closely related meanings:

A physical quantity is said to be Lorentz covariant if it transforms under a given representation of the Lorentz group. According to the representation theory of the Lorentz group, these quantities are built out of scalars, four-vectors, four-tensors, and spinors. In particular, a Lorentz covariant scalar (e.g., the space-ti

Official source

https://en.wikipedia.org/wiki/Lorentz_covariance

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Emergent Lorentz invariance with chiral fermions

Sergey Sibiryakov

We study the renormalization group flow in strongly interacting field theories in the fermion sector corresponding to the transition from theories without a Lorentz invariance at high energies to theories with an approximate Lorentz invariance in the infrared limit. We use the holographic description of the strong coupling. We give special attention to the emergence of chiral fermions in the low-energy limit.

Springer Verlag2016

Constraints on violation of Lorentz invariance from atmospheric showers initiated by multi-TeV photons

Sergey Sibiryakov

Parameterizing hypothetical violation of Lorentz invariance at high energies using the framework of effective quantum field theory, we discuss its effect on the formation of atmospheric showers by very-high-energy gamma rays. In the scenario where Lorentz invariance violation leads to a decrease of the photon velocity with energy the formation of the showers is suppressed compared to the Lorentz invariant case. Absence of such suppression in the high-energy part of spectrum of the Crab nebula measured independently by HEGRA and H.E.S.S. collaborations is used to set lower bounds on the energy scale of Lorentz invariance violation. These bounds are competitive with the strongest existing constraints obtained from timing of variable astrophysical sources and the absorption of TeV photons on the extragalactic background light. They will be further improved by the next generation of multi-TeV gamma-ray observatories.

Iop Publishing Ltd2017

Inflationary perturbations with Lifshitz scaling

Sergey Sibiryakov

Instead of Lorentz invariance, gravitational degrees of freedom may obey Lifshitz scaling at high energies, as it happens in Horava's proposal for quantum gravity. We study consequences of this proposal for the spectra of primordial perturbations generated at inflation. Breaking of 4D diffeomorphism (Diff) invariance down to the foliation-preserving Diff in Horava-Lifshitz (HL) gravity leads to appearance of a scalar degree of freedom in the gravity sector, khronon, which describes dynamics of the time foliation. One can naively expect that mixing between inflaton and khronon will jeopardize conservation of adiabatic perturbations at super Hubble scales. This indeed happens in the projectable version of the theory. By contrast, we find that in the non-projectable version of HL gravity, khronon acquires an effective mass which is much larger than the Hubble scale well before the Hubble crossing time and decouples from the adiabatic curvature perturbation zeta sourced by the inflaton fluctuations. As a result, at super Hubble scales the adiabatic perturbation zeta behaves as in an effectively single field system and its spectrum is conserved in time. Lifshitz scaling is imprinted in the power spectrum of zeta through the modi fied dispersion relation of the inflaton. We point out violation of the consistency relation between the tensor-to-scalar ratio and the spectral tilt of primordial gravitational waves and suggest that it can provide a signal of Lorentz violation in inflationary era.

IOP PUBLISHING LTD2019