Central potential effects induced by Lorentz symmetry violation on modified quantum oscillator field

In this paper, effects of Lorentz symmetry violation determined by a tensor field [Formula: see text] out of the Standard Model Extension on a modified quantum oscillator field in the presence of Cornell-type scalar potential are analyzed. We first introduced a scalar potential [Formula: see text] by modifying the mass square term via transformation [Formula: see text] in the Klein–Gordon equation, and then replace the momentum operator [Formula: see text], where [Formula: see text] is an arbitrary function other than [Formula: see text] to study the modified Klein–Gordon oscillator. We solve the wave equation and obtain the analytical bound-states solutions and see the dependence of oscillator frequency [Formula: see text] on the quantum numbers [Formula: see text] as well as on Lorentz-violating parameters with the potential which shows a quantum effect.

The implications of gamma-ray photons from LHAASO on Lorentz symmetry

The Large High Altitude Air Shower Observatory (LHAASO) has reported the measurement of photons with high energy up to 1.42 PeV from 12 gamma-ray sources. We are concerned with the implications of LHAASO data on the fate of Lorenz symmetry at such high energy level, thus we consider the interaction of the gamma ray with those photons in cosmic microwave background (CMB), and compute the optical depth, the mean free path as well as the survival probability for photons from all these gamma-ray sources. Employing the threshold value predicted by the standard special relativity, it is found that the lowest survival probability for observed gamma ray photons is about 0.60, which is a fairly high value and implies that abundant photons with energy above the threshold value may reach the Earth without Lorentz symmetry violation. We conclude that it is still far to argue that the Lorentz symmetry would be violated due to the present observations from LHAASO. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.

Lorentz Symmetry and High-Energy Neutrino Astronomy

The search of the violation of Lorentz symmetry, or Lorentz violation (LV), is an active research field. The effects of LV are expected to be very small, and special systems are often used to search it. High-energy astrophysical neutrinos offer a unique system to search signatures of LV, due to the three factors: high neutrino energy, long propagation distance, and the presence of quantum mechanical interference. In this brief review, we introduce tests of LV and summarize existing searches of LV, using atmospheric and astrophysical neutrinos.

On the inverse hoop conjecture of Hod

Recently, Hod has shown that Thorne’s hoop conjecture ($$\frac{C(R)}{4\pi M(r\le R)} \le 1\Rightarrow $$ C ( R ) 4 π M ( r ≤ R ) ≤ 1 ⇒ horizon) is violated by stationary black holes and so he proposed a new inverse hoop conjecture characterizing such black holes (that is, horizon $$\Rightarrow \mathcal {H =} \frac{\pi \mathcal {A} }{\mathcal {C}_{{eq} }^{2}} \le 1$$ ⇒ H = π A C eq 2 ≤ 1 ). In this paper, it is exemplified that stationary hairy black holes, endowed with Lorentz symmetry violating Bumblebee vector field related to quantum gravity and dilaton field of string theory, also respect the inverse conjecture. It is shown that stationary hairy singularity, recently derived by Bogush and Galt’sov, does not respect the conjecture thereby protecting it. However, curiously, there are two horizonless stationary wormholes that can also respect the conjecture. Thus one may also state that throat $$\Rightarrow \mathcal {H \le }1$$ ⇒ H ≤ 1 , suggesting that the inverse conjecture may be a necessary but not sufficient proposition.

Salvage of too slow gravitinos

Gravitinos can inherit a non-relativistic dispersion relation while propagating in a background breaking both supersymmetry and Lorentz symmetry spontaneously. This is because the longitudinal mode velocity is controlled by the sound speed in the background. It was pointed out recently by Kolb, Long and McDonough that the production of gravitinos might diverge when this sound speed vanishes. We argue that in the framework of cosmological models with linearly spontaneously broken realised supersymmetry, where the physical fermions are combinations of the vacuum goldstino and the inflatino, the gravitino longitudinal mode has a relativistic dispersion relation and therefore avoids the catastrophic production. We illustrate this in some explicit examples.

Combined Lorentz Symmetry: Lessons from Superfluid $$^3$$He

We consider the possibility of the scenario in which the P, T and Lorentz symmetry of the relativistic quantum vacuum are all the combined symmetries. These symmetries emerge as a result of the symmetry breaking of the more fundamental P, T and Lorentz symmetries of the original vacuum, which is invariant under separate groups of the coordinate transformations and spin rotations. The condensed matter vacua (ground states) suggest two possible scenarios of the origin of the combined Lorentz symmetry, and both are realized in the superfluid phases of liquid $$^3$$ 3 He: the $$^3$$ 3 He-A scenario and the $$^3$$ 3 He-B scenario. In these scenarios, the gravitational tetrads are considered as the order parameter of the symmetry breaking in the quantum vacuum. The $$^3$$ 3 He-B scenarios applied to the Minkowski vacuum lead to the continuous degeneracy of the Minkowski vacuum with respect to the O(3, 1) spin rotations. The symmetry breaking leads to the corresponding topological objects, which appear due to the nontrivial topology of the manifold of the degenerate Minkowski vacua, such as torsion strings. The fourfold degeneracy of the Minkowski vacuum with respect to discrete P and T symmetries suggests that the Weyl fermions are described by four different tetrad fields: the tetrad for the left-handed fermions, the tetrad for the right-handed fermions, and the tetrads for their antiparticles. This may lead to the gravity with several metric fields, so that the parity violation may lead to the breaking of equivalence principle. Finally, we considered the application of the gravitational tetrads for the solution of the cosmological constant problem.