We study possible Lorentz violations by means of gamma-ray bursts (GRB) with special focus on the Large Array Telescope (LAT) of GLAST. We simulate bursts with gtobssim and introduce a Lorentz violating term in the arrival times of the photons. We further perturb these arrival times and energies with a Gaussian distribution corresponding to the time resp. energy resolution of GLAST. We then var...

Lorentz symmetry lies at the heart of relativity and is a feature of low-energy descriptions of nature. Minuscule Lorentz-violating effects arising in theories of quantum gravity offer a promising candidate signal for new physics at the Planck scale. A framework is presented for incorporating Lorentz violation into general relativity and other theories of gravity. Applying this framework yields...

Many properties of H-unitary and Lorentz matrices are derived using elementary methods. Complex matrices which are unitary with respect to the indefinite inner product induced by an invertible Hermitian matrix H, are called H-unitary, and real matrices that are orthogonal with respect to the indefinite inner product induced by an invertible real symmetric matrix, are called Lorentz. The focus i...

Orlicz–Lorentz spaces provide a common generalization of Orlicz spaces and Lorentz spaces. In this paper, we investigate their Boyd indices. Bounds on the Boyd indices in terms of the Matuszewska–Orlicz indices of the defining functions are given. Also, we give an example to show that the Boyd indices and Zippin indices of an Orlicz–Lorentz space need not be equal, answering a question of Malig...

We study possible crossing of the phantom divided barrier in a Lorentz invariance violating dark energy model. Lorentz invariance violation which is achieved by introducing a vector field in the action, incorporates directly in the dynamics of the scalar field and equation of state. This interesting feature allows us to study phantom divided barrier crossing in the context of Lorentz invariance...

It has been almost 100 years since Einstein formulated his special theory of relativity in 1905. He showed that the basic space–time symmetry is dictated by the Lorentz group. It is shown that this group of Lorentz transformations is not only applicable to special relativity, but also constitutes the scientific language for optical sciences. It is noted that coherent and squeezed states of ligh...

We construct classes of two-dimensional aperiodic Lorentz systems that have infinite horizon and are ‘chaotic’, in the sense that they are (Poincaré) recurrent, uniformly hyperbolic and ergodic, and the first-return map to any scatterer is K-mixing. In the case of the Lorentz tubes (i.e., Lorentz gases in a strip), we define general measured families of systems (ensembles) for which the above p...

Using the conservation of energy and momentum during collisions of any two shells, we consider the efficiency of gamma-ray bursts by assuming that the ejecta from the central engine are equally massive and have the same Lorentz factors. We calculate the efficiency and the final Lorentz factor of the merged whole shell for different initial diversities of Lorentz factors and for different micros...

We reconsider the role of Lorentz invariance in the dynamical generation of the observed internal symmetries. We argue that, generally, Lorentz invariance can be imposed only in the sense that all Lorentz noninvariant effects caused by the spontaneous breakdown of Lorentz symmetry are physically unobservable. The application of this principle to the most general relativistically invariant Lagra...

We study Lorentz violation effects to flavor transitions of high energy astrophysical neutrinos. It is shown that the appearance of Lorentz violating Hamiltonian can drastically change the flavor transition probabilities of astrophysical neutrinos. Predictions of Lorentz violation effects to flavor compositions of astrophysical neutrinos arriving on Earth are compared with IceCube flavor compos...