Narrow Results

A generalization at finite temperature of the scalar Myers–Pospelov quantum field theory with mass dimension five operators that break Lorentz symmetry is considered. In particular, we introduce a thermal vacuum and a doubled Hilbert space within the formalism of Thermo Field Dynamics (TFD) to account for extended quantum field effects. The higher-order operators in the effective Lagrangian give rise to negative-metric modes, which are treated using a perturbative method. The perturbative modes that propagate correspond to standard second-order equations of motion with Lorentz-violating modifications without altering the number of degrees of freedom. In this perturbative, Lorentz-violating TFD framework, we investigate the finite-temperature effects, including thermal fluctuations and size effects.

We study the Lorentz and CPT violating effects on the ratio where BR_LorVio (BR_SM) is the branching ratios coming from the Lorentz violating effects (the SM), for the decays H⁰→f⁺f^- (f = quarks and charged leptons) and H⁰→ZZ(W⁺W^-). We observe that these new effects are too small to be detected, especially for f⁺f^- output, since the corresponding coefficients are highly suppressed at the low energy scale.

Contrary to what is often stated, a fundamental spacetime discreteness need not contradict Lorentz invariance. A causal set's discreteness is in fact locally Lorentz invariant, and we recall the reasons why. For illustration, we introduce a phenomenological model of massive particles propagating in a Minkowski spacetime which arises from an underlying causal set. The particles undergo a Lorentz invariant diffusion in phase space, and we speculate on whether this could have any bearing on the origin of high energy cosmic rays.

We investigate potential quantum nonlinear corrections to Dirac's equation through its sub-leading effect on neutrino oscillation probabilities. Working in the plane-wave approximation and in the μ - τ sector, we explore various classes of nonlinearities, with or without an accompanying Lorentz violation. The parameters in our models are first delimited by current experimental data before they are used to estimate corrections to oscillation probabilities. We find that only a small subset of the considered nonlinearities has the potential to be relevant at higher energies and thus possibly detectable in future experiments. A falsifiable prediction of our models is an energy-dependent effective mass-squared, generically involving fractional powers of the energy.

Lorentz violation (LV) is predicted by some quantum gravity (QG) candidates, wherein the canonical energy–momentum dispersion relation, E² = p²+m², is modified. Consequently, new phenomena beyond the standard model are predicted. In particular, the presence of LV highly affects the propagation of astrophysical photons with very high energies from distant galaxies. In this paper, we review the updating theoretical and experimental results on this topic. We classify the effects into three categories: (i) time lags between photons with different energies; (ii) a cutoff of photon flux above the threshold energy of photon decay, γ→e⁺+e^-; (iii) new patterns in the spectra of multi-TeV photons and EeV photons, due to the absorption of background lights. As we can see, the details of LV effects on astrophysical photons depend heavily on the "phase space" of LV parameters. From observational aspects, available and upcoming instruments can study these phenomena hopefully, and shed light onto LV issues and QG theories. The most recent progresses and constraints on the ultra-high energy cosmic rays (UHECRs) are also discussed.

Violation of Lorentz invariance and CPT symmetry is a predicted phenomenon of Planck-scale physics. Various types of data are analyzed to search for Lorentz violation under the Standard Model Extension (SME) framework, including neutrino oscillation data. MiniBooNE is a short-baseline neutrino oscillation experiment at Fermilab. The measured excesses from MiniBooNE cannot be reconciled within the neutrino Standard Model (νSM); thus it might be a signal of new physics, such as Lorentz violation. We have analyzed the sidereal time-dependence of MiniBooNE data for signals of the possible breakdown of Lorentz invariance in neutrinos. In this brief review, we introduce Lorentz violation, the neutrino sector of the SME and the analysis of short-baseline neutrino oscillation experiments. We then present the results of the search for Lorentz violation in MiniBooNE data. This review is based on the published result.

Recently Kahniashvili et al.⁹ presented a unified treatment for ultraviolet Lorentz violation (LV) testing through electromagnetic wave propagation in magnetized plasmas, based on dispersion and rotation measured data. Based on the fact discovered recently by Kostelecky et al., ³ that LV may place constraints on spacetime torsion, in this paper it is shown that on the limit of very low frequency torsion waves, it is possible to constraint torsion from Faraday rotation and CMB on a similar fashion as Minkowski spacetime plus torsion. Here, the Maxwells modified equations are obtained by a perturbative method introduced by de Sabbata and Gasperini [Introduction to Gravitation (World Scientific, 1980)]. Torsion is constraint to Q_CMB≈10^-18GeV which is not so stringent as the 10^-31GeV obtained by Kostelecky et al. However, Gamma-Ray Bursts (GRBs) may lead to the more string value obtained by Kostelecky et al.Another interesting constraint on torsion is shown to be placed by galactic dynamo seed magnetic fields. For torsion effects be compatible with the galactic dynamo seeds, one obtains a torsion constraint of 10^-33GeV which is two orders of magnitude more stringent that the above Kostelecky et al. limit.

I present a brief review on space and time in different periods of physics, and then talk on the nature of space and time from physical arguments. I discuss the ways to test such a new perspective on space and time through searching for Lorentz violation in some physical processes. I also make an introduce to a newly proposed theory of Lorentz violation from basic considerations.

The action for a (3+1)-dimensional particle in very special relativity (VSR) is studied. It is proved that massless particles only travel in effective (2+1)-dimensional spacetime. It is remarkable that this action can be written as an action for a relativistic particle in a background gauge field and it is shown that this field causes the dimensional reduction. A new symmetry for this system is found. Furthermore, a general action with restored Lorentz symmetry is proposed for this system. It is shown that this new action contains VSR and two-time physics.

Here, we consider a gravity theory involving a spontaneous Lorentz symmetry breaking called the bumblebee model. We show that, at certain values of the bumblebee field, the Gödel metric is consistent within this theory.

The observation of gravitational waves from the Laser Interferometer Gravitational-Wave Observatory (LIGO) event GW150914 may be used to constrain the possibility of Lorentz violation in graviton propagation, and the observation by the Fermi Gamma-Ray Burst Monitor (GBM) of a transient source in apparent coincidence may be used to constrain the difference between the velocities of light and gravitational waves: $c_g-c_{\gamma }<10^{-17}$.

Gravitoelectromagnetism (GEM) is an approach for the gravitation field that is described using the formulation and terminology similar to that of electromagnetism. The Lorentz violation is considered in the formulation of GEM that is covariant in its form. In practice, such a small violation of the Lorentz symmetry may be expected in a unified theory at very high energy. In this paper, a non-minimal coupling term, which exhibits Lorentz violation, is added as a new term in the covariant form. The differential cross-section for Bhabha scattering in the GEM framework at finite temperature is calculated that includes Lorentz violation. The Thermo Field Dynamics (TFD) formalism is used to calculate the total differential cross-section at finite temperature. The contribution due to Lorentz violation is isolated from the total cross-section. It is found to be small in magnitude.

This work presents an experimental test of Lorentz invariance violation in the infrared (IR) regime by means of an invariant minimum speed in spacetime and its effects on the time when an atomic clock given by a certain radioactive single-atom (e.g. isotope Na${}^{25}$) is a thermometer for an ultracold gas like the dipolar gas Na${}^{23}$K${}^{40}$. So, according to a Deformed Special Relativity (DSR) so-called Symmetrical Special Relativity (SSR), where there emerges an invariant minimum speed V in the subatomic world, one expects that the proper time of such a clock moving close to V in thermal equilibrium with the ultracold gas is dilated with respect to the improper time given in lab, i.e. the proper time at ultracold systems elapses faster than the improper one for an observer in the lab, thus leading to the so-called proper time dilation so that the atomic decay rate of an ultracold radioactive sample (e.g. Na${}^{25}$) becomes larger than the decay rate of the same sample at room temperature. This means a suppression of the half-life time of a radioactive sample thermalized with an ultracold cloud of dipolar gas to be investigated by NASA in the Cold Atom Lab (CAL).

This research aims to provide the geometrical foundation of the uncertainty principle within a new causal structure of spacetime so-called Symmetrical Special Relativity (SSR), where there emerges a Lorentz violation due to the presence of an invariant minimum speed $V$ related to the vacuum energy. SSR predicts that a dS scenario occurs only for a certain regime of speeds $v$, where $v<v_0=\sqrt{cV}$, which represents the negative gravitational potentials ($\mathrm{\Phi }<0$) connected to the cosmological parameter $\mathrm{\Lambda }>0$. For $v=v_0$, Minkowski (pseudo-Euclidean) space is recovered for representing the flat space ($\mathrm{\Lambda }=0$), and for $v>v_0$ ($\mathrm{\Phi }>0$), Anti-de Sitter (AdS) scenario prevails ($\mathrm{\Lambda }<0$). The fact that the current universe is flat as its average density of matter distribution (${\rho }_m$ given for a slightly negative curvature $R$) coincides with its vacuum energy density (${\rho }_{\mathrm{\Lambda }}$ given for a slightly positive curvature $\mathrm{\Lambda }$), i.e. the cosmic coincidence problem, is now addressed by SSR. SSR provides its energy–momentum tensor of perfect fluid, leading to the EOS of vacuum ($p=-{\rho }_{\mathrm{\Lambda }}$). Einstein equation for vacuum given by such SSR approach allows us to obtain ${\rho }_{\mathrm{\Lambda }}$ associated with a scalar curvature $\mathrm{\Lambda }$, whereas the solution of Einstein equation only in the presence of a homogeneous distribution of matter ${\rho }_m$ for the whole universe presents a scalar curvature $R$, in such a way that the presence of the background field $\mathrm{\Lambda }$ opposes the Riemannian curvature $R$, thus leading to a current effective curvature $R_{\mathrm{\text{eff}}}=R+\mathrm{\Lambda }\approx 0$ according to observations. This corrects the notion of gravity as being only of Riemannian origin as the flat space has connection with a background gravity. In view of the current dS scenario with a quasi-zero $\mathrm{\Lambda }$ slightly larger than $\left|R\right|$, we will just obtain a Generalized Uncertainty Principle (GUP) given in the cases of weak gravity and anti-gravity.

A formal analogy between the gravitational and the electromagnetic fields leads to the notion of Gravitoelectromagnetism (GEM) to describe gravitation. A Lagrangian formulation for GEM is developed for scattering processes with gravitons as an intermediate state, in addition to photons for electromagnetic scattering. The differential cross section is calculated for gravitational Möller scattering based on GEM theory. This gravitational cross section is obtained for cases where the Lorentz symmetry is maintained or violated. The Lorentz violation is introduced with the non-minimal coupling term. In addition, using the Thermo Field Dynamics formalism, thermal corrections to the differential cross section are investigated. By comparing the electromagnetic and GEM versions, of Möller scattering, it is shown that the gravitational effect may be measured at an appropriate energy scale.

This paper is devoted to the study of interactions between stationary electromagnetic sources for the minimal and nonminimal CPT-odd photon sector of the Standard Model Extension (SME), where we search mainly for physical phenomena not present in the Maxwell electrodynamics. First, we consider the minimal CPT-odd sector, where the Lorentz violation is caused by the Carroll–Field–Jackiw (CFJ) term, namely, $\sim {𝜖}^{\mu \nu \alpha \beta }{(k_{AF})}_{\mu }{A}_{\nu }{F}_{\alpha \beta }$, and we treat the Lorentz breaking parameter ${(k_{AF})}^{\mu }$ perturbatively up to second order. We consider effects due to the presence of point-like charges, Dirac strings and point-like dipoles. In special, we calculate the electromagnetic field produced outside the string and investigate the so-called Aharonov–Bohm bound states in Lorentz violation context. Afterwards, we consider a model where the Lorentz violation is generated by the higher-derivative version of the CFJ model, namely, $\sim {𝜖}^{\mu \nu \alpha \beta }{V}_{\mu }{A}_{\nu }\square F_{\alpha \beta }$, which is a dimension five term of the CPT-odd sector of the nonminimal SME. For this higher-derivative model, we obtain effects up to second order in $V^{\mu }$ related to the presence of point-like charges and a steady current line. We use overestimated constraints for the Lorentz violation parameters in order to investigate the physical relevance of some results found in atomic systems. We also make an overestimate for the background vectors using experimental data from the atomic electric field.

The recent reported Glashow resonance (GR) event shows a promising prospect in the test of the Lorentz violation (LV) by the high-energy astrophysical neutrinos (HANs) around the resonant energy. However, since the production source and the energy spectra of HANs are uncertain at present, moderate LV effects may be concealed at the TeV energy-scale. In this paper, we propose the LV Hamiltonian of a special texture which can lead to the decoupling of ${\nu }_{\mu }({\bar{\nu }}_{\mu })$. On the base of the decoupling, a noticeable damping of the GR event rate is shown for the HANs from the source dominated by ${\bar{\nu }}_{\mu }$, irrespective of the energy spectra of the HANs at Earth. Accordingly, the observation of GR events may bring stringent constraints on the LV and the production mechanism of HANs.

The influence of Lorentz- and CPT-violating terms (in "vector" and "axial vector" couplings) on the Dirac equation is explicitly analyzed: plane-wave solutions, dispersion relations and eigenenergies are explicitly obtained. The nonrelativistic limit is worked out and the Lorentz-violating Hamiltonian identified in both cases, in full agreement with the results already established in the literature. Finally, the physical implications of this Hamiltonian on the spectrum of hydrogen are evaluated both in the absence and presence of a magnetic external field. It is observed that the fixed background, when considered in a vector coupling, yields no qualitative modification in the hydrogen spectrum, whereas it does provide an effective Zeeman-like splitting of the spectral lines whenever coupled in the axial vector form. It is also argued that the presence of an external fixed field does not imply new modifications on the spectrum.

A planar Maxwell–Chern–Simons–Proca model endowed with a Lorentz-violating background is taken as framework to investigate the electron–electron interaction. The Dirac sector is introduced exhibiting a Yukawa and a minimal coupling with the scalar and the gauge fields, respectively. The electron–electron interaction is then exactly evaluated as the Fourier transform of the Möller scattering amplitude (carried out in the nonrelativistic limit) for the case of a purely timelike background. The interaction potential exhibits a totally screened behavior far from the origin as consequence of massive character of the physical mediators. The total interaction (scalar plus gauge potential) can always be attractive, revealing that this model may lead to the formation of electron–electron bound states.

We derive a modified dispersion relation (MDR) in the Lorentz violation extension of the quantum electrodynamics (QED) sector in the standard model extension (SME) framework. Based on the extended Dirac equation and corresponding MDR, we observe the resemblance of the Lorentz violation coupling to spin–gravity coupling. We also develop a neutrino oscillation mechanism induced by the presence of nondiagonal terms of Lorentz violation couplings in two-flavor space in a two-spinor formalism by explicitly assuming neutrinos to be Marjorana fermions. We also obtain a very stringent bound (∽ 10^-25) on one of the Lorentz violation parameters by applying the MDR to the ultrahigh energy cosmic ray (UHECR) problem.