arXiv subjects

Zhi Xiao

Publications and source records attributed to Zhi Xiao.

18 recordsLinked to original sources

arXiv2026

Hamiltonian Constraints on Spontaneous Lorentz Symmetry Breaking in the Bumblebee Model

This study demonstrates that the common practice of determining spontaneous Lorentz violation via the minimum of a Lagrangian potential is generally incorrect. By analyzing the Hamiltonian structure and constraints of vector fields, we show that the true vacuum must be derived from the Hamiltonian density. We prove that the standard quadratic potential cannot consistently generate a vacuum expectation value (VEV), identifying a cubic potential as the simplest viable alternative. Furthermore, we prove that smooth potentials only support stable timelike or lightlike VEVs. These conclusions extend to higher-rank tensor fields and impose rigorous consistency constraints on higher-rank tensor fields and Lorentz-violating effective field theories.

hep-ph↗

arXiv2026

Maxwell theories along the light track: Null Formalism in extended electrodynamics

We develop a differential-form approach to systematically derive the Newman-Penrose null-tetrad equations for Lorentz-violating extensions of Maxwell electrodynamics. The coordinate-independent nature of differential forms allows the actions and corresponding field equations of the theory to be expressed compactly and enables a systematic and transparent derivation of first-order equations in the Newman-Penrose formalism. Within this formalism, we explicitly present a simple algebraic construction for the gauge invariant extended Maxwell actions that avoids explicit index manipulations up to mass dimension six. The combined scheme of differential-form approach and Newman-Penrose formalism offers an efficient tool for analyzing Lorentz-violating effects on asymptotic photon propagation and polarization.

hep-ph↗

arXiv2026

Constraints on birefringence-free photon theory within standard-model extension

Constraints on the birefringence-free subset of Lorentz-violating (LV) operators are derived using 14 GRB photons in the GeV-band. These constraints target the isotropic $c_{(I)00}^{(d)}$ coefficients for dimensions $d=6,8,10$ within the framework of the Standard-Model Extension (SME). Employing theory-agnostic Bayesian parameter estimation methods, our analysis indicates a preference for subluminal LV effects. Focusing on this case, we further refine the parameter constraints, yielding results that are mutually consistent. Within the 95\% posterior credible interval, our constraints yield the bounds, $|c_{(I)00}^{(6)}|\le7.75 \times 10^{-20} ~ {\rm GeV}^{-2}$, $|c_{(I)00}^{(8)}|\le4.92 \times 10^{-24} ~ {\rm GeV}^{-4}$, and $|c_{(I)00}^{(10)}|\le3.46 \times 10^{-28} ~ {\rm GeV}^{-6}$, which improve upon the most stringent credible-interval bounds reported in the literature by at least five orders of magnitude.

hep-ph↗

arXiv2025

Analytical solutions of CPT-odd Maxwell equations in Schwarzschild spacetime

In this work, we present the CPT-violating (CPTV) Maxwell equations in curved spacetime using the Newman-Penrose (NP) formalism. We obtain a semi-analytical solution to the Maxwell equations in Schwarzschild spacetime under the assumption that the CPT-odd $\left(k_{AF}\right)^μ$ term exhibits spherical symmetry in the Schwarzschild background. Retaining only terms up to linear order in the $\left(k_{AF}\right)^μ$ coefficient, we obtain perturbative solutions by treating the solutions of the Lorentz-invariant Maxwell equations as the zeroth-order approximation and incorporating the $\left(k_{AF}\right)^μ$ terms as an additional source term alongside the external charge current. Each resulting NP scalar field can be factorized into two components: the radial component is expressed in terms of hypergeometric functions, while the angular component is described by spin-weighted spherical harmonics.

gr-qc↗

arXiv2025

The asymptotic behavior of Lorentz-violating photon fields

In this work, we derive the Newman-Penrose formalism of Maxwell's equations using two approaches: differential forms and intrinsic derivatives. Denoting $(k_{AF})^μ$ as $k^μ$, with $k^μ=(k^t,k^r,0,0)$ in spherically symmetric spacetimes, we show that the expansion in $r^{-1}$ fails to produce consistent, closed solutions due to the inability to separate Lorentz-violating (LV) phase factors, as the Lorentz-invariant (LI) null tetrad does not adapt to the LV wavefront. Moreover, with exact formal solutions, we demonstrate that the expansion is nonperturbative in the LV parameter $k^2\equiv k^t-k^r$. For $r\gg1/k^2$, higher powers of $k^2$ dominate over lower powers, as the latter decay more rapidly with increasing $r$. Although the Coulomb mode $ϕ_1\sim\mathcal{O}(\ln{r}/r^2)$ deviates from the LI expectation $\mathcal{O}(r^{-2})$ due to LV corrections, the leading outgoing radiation mode remains unaffected, i.e., $ϕ_2\sim\mathcal{O}(r^{-1})$. Given the constraint $|k_{AF}|\le10^{-44}$GeV \cite{CMBLV-N}, the three complex scalars $ϕ_a$ ($a=0,1,2$) still obey the peeling theorem: $ϕ_a\sim\mathcal{O}(r^{(a-3)}),~a=0,1,2$ for large, finite distances.

hep-ph↗

arXiv2022

The analogy of the Lorentz-violating fermion-gravity and fermion photon couplings

By adopting a methodology proposed by R.J. Adler \etl, we study the interesting analogy between the fermion-gravity and the fermion-electromagnetic interactions in the presence of the minimal Lorentz-violating (LV) fermion coefficients. The one-fermion matrix elements of gravitational interaction (OMEGI) are obtained with a prescribed Lense-Thirring (LT) metric assuming test particle assumption. Quite distinct from the extensively studied linear gravitational potential, the LT metric is an essentially curved metric, and thus reveals the anomalous LV matter-gravity couplings as a manifestation of the so-called gravito-magnetic effects, which go beyond the conventional equivalence principle predictions. By collecting all the spin-dependent operators from the OMEGI with some reasonable assumptions, we get a LV non-relativistic Hamiltonian, from which we derive the anomalous spin precession and gravitational acceleration due to LV. Combined these results with certain spin gravity experiments, we get some rough bounds on several LV parameters, such as $|3\vec{\tilde{H}}-2\vec{b}|\leq1.46\times10^{-5}\mathrm{eV}$, with some ad hoc assumptions.

hep-ph↗

arXiv2020

The neutron returning time in a linear potential

In this paper, we calculate the quantum time delays for neutron scattering off the Earth's linear gravitational potential. The quantum time delays are obtained by subtracting the classical returning time (CRT) from the Wigner time, the dwell time and the redefined Larmor time respectively. Different from the conventional definition, our Larmor time is defined by aligning the magnetic field along the neutron propagation direction, and this definition does give reasonable results for motions through a free region and a square barrier. It is worth noting that in the zero magnetic field limit, the Larmor time coincides well with the CRT, which is due to the special shape of linear barrier, and may have some relevance to the weak equivalence principle. It is also found that the classical forbidden region plays an essential role for the dwell time $τ_{_\mathrm{DW}}$ to match with the CRT, and the difference between the dwell and the phase times, \ie, the self-interference time delay, is barrier shape sensitive and clearly shows the peculiarity of the linear barrier. All the time delays are on the order of sub-millisecond and exhibit oscillating behaviors, signaling the self-interference of the scattering neutron, and the oscillations become evident only when the de Broglie wavelength $λ_k=2π/k$ is comparable to the characteristic length $L_c=[2m^2g/\hbar^2]^{-1/3}$. If the time delay measurement is experimentally realizable, it can probe the quantum nature for particle scattering off the gravitational potential in the temporal domain.

quant-ph↗

arXiv2020

The CPT-violating effects on neutrons' gravitational bound state

In this work, the CPT-violating (CPTV) interactions on neutrons' gravitational bound state are studied. With simple analytical solutions, we provide a preliminary investigation on the Lorentz-violation (LV) induced spin precession due to the $\vecσ\cdot\vec{\tilde{b}}(1+gz)$ and $\bar{b}/m_{_I}\vecσ\cdot\hat{\vec{p}}$ couplings, where $\vec{\tilde{b}}$ and $\bar{b}$ represent LV coefficients. The helicity-dependent couplings can induce unusual phase evolutions with position and momentum dependence. As $\vec{\tilde{b}}$ varies with time due to the Earth's motion, the spin polarization also shows a sidereal time dependence, and it may be enhanced with time for ultra-stable polarized state of neutrons. The inseparability of the spin-momentum coupling of the $\bar{b}$-term can also lead to motional dependent polarization state. With the precisely measured transition frequency between different gravitational bound states, we get a rough bound $|\vec{\tilde{b}}|<3.9\times10^{-3}$GeV for unpolarized neutrons. If the spin-flip transition frequency can reach comparable precision in the future, the bound can be improved to the level of $10^{-24}$GeV. The test of weak equivalence principle with polarized atom may also improve it significantly.

hep-ph↗

arXiv2019

The CPT-violating effects on neutron's gravitational bound state

Analytical solutions with effective CPT-violating spin--gravity corrections to the neutron's gravitational bound states are obtained. The helicity-dependent phase evolution due to $\vecσ\cdot\vec{\tilde{b}}$ and $\vecσ\cdot\hat{\vec{p}}$ couplings not only leads to spin precession, %shown by the tip of the spin on the Bloch sphere,but also to transition-frequency shifts between different gravitational bound states. Utilizing transition frequencies measured in the qBounce experiment,\cite{GRS} we obtain the rough bound $|\vec{\tilde{b}}|<6.9\times10^{-21}$GeV. Incorporating known systematic errors may lead to more robust and tighter constraints.

hep-ph↗

arXiv2018

Lorentz-violating scalar Hamiltonian and equivalence principle in a static metric

In this paper, we obtain a nonrelativistic Hamiltonian from the Lorentz-violating (LV) scalar Lagrangian in the minimal SME. The Hamiltonian is obtained by two different methods. One is through the usual ansatz $Φ(t,\vec{r})=e^{-imt}Ψ(t,\vec{r})$ applied to the LV corrected Klein-Gordon equation, and the other is the Foldy-Wouthuysen transformation. The consistency of our results is also partially supported by the comparison with the spin-independent part of the fermion Hamiltonian. In this comparison, we can also establish a relation between the set of scalar LV coefficients with their fermion counterparts. Using a pedagogical definition of the weak equivalence principle (WEP), we further point out that the LV Hamiltonian not only necessarily violates universal free fall, which is clearly demonstrated in the geodesic deviation, but also violates WEP in a semi-classical setting. As a bosonic complement, this method can be straightforwardly applicable to the spin-1 case, which shall be useful in the analysis of atomic tests of WEP, such as the case of the $^{87}\text{Rb}_1$ atom.

hep-ph↗

arXiv2018

Robust and Efficient Boosting Method using the Conditional Risk

Well-known for its simplicity and effectiveness in classification, AdaBoost, however, suffers from overfitting when class-conditional distributions have significant overlap. Moreover, it is very sensitive to noise that appears in the labels. This article tackles the above limitations simultaneously via optimizing a modified loss function (i.e., the conditional risk). The proposed approach has the following two advantages. (1) It is able to directly take into account label uncertainty with an associated label confidence. (2) It introduces a "trustworthiness" measure on training samples via the Bayesian risk rule, and hence the resulting classifier tends to have finite sample performance that is superior to that of the original AdaBoost when there is a large overlap between class conditional distributions. Theoretical properties of the proposed method are investigated. Extensive experimental results using synthetic data and real-world data sets from UCI machine learning repository are provided. The empirical study shows the high competitiveness of the proposed method in predication accuracy and robustness when compared with the original AdaBoost and several existing robust AdaBoost algorithms.

stat.ML↗

arXiv2017

Constraining Spacetime Nonmetricity with Neutron Spin Rotation in Liquid He-4

General spacetime nonmetricity coupled to neutrons is studied. In this context, it is shown that certain nonmetricity components can generate a rotation of the neutron's spin. Available data on this effect obtained from slow-neutron propagation in liquid helium are used to constrain isotropic nonmetricity components at the level of $10^{-22}\,$GeV. These results represent the first limit on the nonmetricity $ζ^{(6)}_2S_{000}$ parameter as well as the first measurement of nonmetricity inside matter.

hep-ph↗

arXiv2016

The Impact of Lorentz Violation on the Klein Tunneling Effect

We discuss the impact of a tiny Lorentz-violating $b^μ$ term on the one dimensional motion of a Dirac particle scattering on a rectangular barrier. We assume the experiment is performed in a particular inertial frame, where the components of $b^μ$ are assumed constants. The results show that Lorentz-violation modification to the transmission rate depends on the observer Lorentz nature of $b^μ$. For a spacelike or lightlike $b^μ$ the induced resonant frequency shift depends on the polarization, while for timelike $b^μ$ there is essentially no modification.

hep-ph↗

arXiv2012

Revisiting 1-Dimensional Double-Barrier Tunneling in Quantum Mechanics

This paper revisited quantum tunneling dynamics through a square double-barrier potential. We emphasized the similarity of tunneling dynamics through double-barrier and that of optical Fabry--P$\acute{e}$rot (FP) interferometer. Based on this similarity, we showed that the well-known resonant tunneling can also be interpreted as a result of matter multi-wave interference, analogous to that of FP interferometer. From this analogy, we also got an analytical finesse formula of double-barrier. Compared with that obtained numerically for a specific barrier configuration, we found that this formula works well for resonances at "deep tunneling region". Besides that, we also calculated standing wave spectrum inside the well of double barriers and phase time of double-barrier tunneling. The wave number spectrums of standing wave and phase time show another points of view on resonance. From semi-numerical calculations, we interpreted the peak of phase time at resonance as resonance life time, which coincides at least in order of magnitude with that obtained from uncertainty principle. Not to our surprise, phase time of double-barrier tunneling also saturates at long barrier length limit $l\rightarrow\infty$ as that of tunneling through a single barrier, and the limits are the same.

quant-ph↗

arXiv2010

Eikonal equation of the Lorentz-violating Maxwell theory

We derive the eikonal equation of light wavefront in the presence of Lorentz invariance violation (LIV) from the photon sector of the standard model extension (SME). The results obtained from the equations of $\mathbf{E}$ and $\mathbf{B}$ fields respectively are the same. This guarantees the self-consistency of our derivation. We adopt a simple case with only one non-zero LIV parameter as an illustration, from which we find two points. One is that, in analogy with Hamilton-Jacobi equation, from the eikonal equation, we can derive dispersion relations which are compatible with results obtained from other approaches. The other is that, the wavefront velocity is the same as the group velocity, as well as the energy flow velocity. If further we define the signal velocity $v_s$ as the front velocity, there always exists a mode with $v_s>1$, hence causality is violated classically. Thus our method might be useful in the analysis of Lorentz violation in QED in terms of classical causality .

hep-th↗

arXiv2010

Lorentz violation from cosmological objects with very high energy photon emissions

Lorentz violation (LV) is predicted by some quantum gravity theories, where photon dispersion relation is modified, and the speed of light becomes energy-dependent. Consequently, it results in a tiny time delay between high energy photons and low energy ones. Very high energy (VHE) photon emissions from cosmological distance can amplify these tiny LV effects into observable quantities. Here we analyze four VHE $γ$-ray bursts (GRBs) from Fermi observations, and briefly review the constraints from three TeV flares of active galactic nuclei (AGNs) as well. One step further, we present a first robust analysis of VHE GRBs taking the intrinsic time lag caused by sources into account, and give an estimate to quantum gravity energy $\sim 2 \times 10^{17}$ GeV for linear energy dependence, and $\sim 5 \times 10^9$ GeV for quadratic dependence. However, the statistics is not sufficient due to the lack of data, and further observational results are desired to constrain LV effects better.

hep-ph↗

arXiv2010

Constraints on Lorentz invariance violation from gamma-ray burst GRB090510

We obtain modified dispersion relations by requiring the vanishing of determinant of inverse of modified photon propagators in Lorentz invariance violation (LIV) theory. Inspired by these dispersion relations, we give a more general dispersion relation with less assumption and apply it to the recent observed gamma-ray burst GRB090510 to extract various constraints on LIV parameters. We find that the constraint on quantum gravity mass is slightly larger than the Planck mass but is consistent with the other recent observations, so the corresponding LIV coefficient $ξ_1$ has reached the natural order ($o(1)$) as one expects. From our analysis, the linear LIV corrections to photon group velocity might be not excluded yet.

hep-ph↗

arXiv2009

Lorentz violation dispersion relation and its application

We derive a modified dispersion relation (MDR) in the Lorentz violation extension of 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 with spin-gravity coupling. We also develop a neutrino oscillation mechanism induced by the presence of nondiagonal terms of Lorentz violation couplings in 2-flavor space in a 2-spinor formalism by explicitly assuming neutrinos to be Marjorana fermions. We also obtain a much stringent bound ($\backsim10^{-25}$) on one of the Lorentz violation parameters by applying MDR to the ultrahigh energy cosmic ray (UHECR) problem.

hep-ph↗