Imaginary Weyl coordinates in the Kerr space-time

By introducing imaginary Weyl coordinates the Kerr geometry can be described by the Weyl coordinate system as good as the Boyer-Lindquist system.     

The neutrino energy-momentum tensor and the Weyl equations in curved space-time

In general, a first order Lagrangian gives rise to second order Euler-Lagrange equations. However, there are important examples where the associated Euler-Lagrange equations are of first order only, the Weyl neutrino equations being of this type. In this paper we therefore consider first order spinor Lagrangians which give rise to firstorder Euler-Lagrange equations. Specifically, the most general first order spinor field equations of rank one in curved space-time which are derivable from a first order Lagrangian of the same type are explicitly constructed. Subject to a certain restriction, the Weyl neutrino equation is the only possibility. Furthermore, if the spinor field satisfies the Weyl neutrino equation, then the associated energy momentum tensor is the conventional neutrino energymomentum tensor.     

Separation of variables and quantum numbers for Weyl neutrino fields on curved space-time

We construct, via separation of variables, a first-order differential operator whose commutator with the Weyl neutrino operator is proportional to it in the class \(\mathfrak{D}\) of Petrov type D vacuum and electrovac backgrounds with cosmological constant. Further, we characterize tensorially all such operators on an arbitrary background space-time. These results when combined explain the existence of a two-index Killing spinor in the class \(\mathfrak{D}\) .     

Clocks in nonstandard synchrony

This paper recalls the mathematical conditions to which the connecting parameters of any finite set of synchronized isochronous clocks are subject and presents the general solution of the light-signal round-trip equations. It concludes with remarks on nonstandard synchrony of infinite sets of clocks.     

Clocks and gravity

We consider the assumption that clocks measure proper time-that is, in a gravitational field ideal clocks are governed by the equationds ²=g _ij dxⁱ dx^j-and give some theoretical and experimental constraints on clock measurements. In particular, we find that if we assume that clocks are governed by an equation of the formds ⁴=c _ijkl dxⁱ dx^j dx^k dx^l, then this equation must reduce to the quadratic equation in a weak, spherically symmetric, static gravitational field (at least to first order in the Newtonian gravitational potentialU), otherwise additional contributions to the time-delay effect of radar propagation (that are not observed) are predicted.     

Weyl geometry

We develop the properties of Weyl geometry, beginning with a review of the conformal properties of Riemannian spacetimes. Decomposition of the Riemann curvature into trace and traceless parts allows an easy proof that the Weyl curvature tensor is the conformally invariant part of the Riemann curvature, and shows the explicit change in the Ricci and Schouten tensors required to insure conformal invariance. We include a proof of the well-known condition for the existence of a conformal transformation to a Ricci-flat spacetime. We generalize this to a derivation of the condition for the existence of a conformal transformation to a spacetime satisfying the Einstein equation with matter sources. Then, enlarging the symmetry from Poincaré to Weyl, we develop the Cartan structure equations of Weyl geometry, the form of the curvature tensor and its relationship to the Riemann curvature of the corresponding Riemannian geometry. We present a simple theory of Weyl-covariant gravity based on a curvature-linear action, and show that it is conformally equivalent to general relativity. This theory is invariant under local dilatations, but not the full conformal group.     

Weyl gravitoelectromagnetism

We study the gauge transformation in the context of gravitoelectromagnetism and introduce a new expression for the phase factor. Using these concepts and with the principle of local gauge invariance applied to physical theories, a formal derivation of gravitoelectromagnetism is obtained.     

Re-explanation of Weyl Quantization Scheme via Weyl Ordering Approach

We re-explain the Weyl quantization scheme by virtue of the technique of integration within Weyl ordered product of operators, i.e., the Weyl correspondence rule can be reconstructed by classical functions＇ Fourier transformation followed by an inverse Fourier transformation within Weyl ordering of operators. As an application of this reconstruction, we derive the quantum operator coresponding to the angular spectrum amplitude of a spherical wave.     

Re-explanation of Weyl Quantization Scheme via Weyl Ordering Approach

We re-explain the Weyl quantization scheme by virtue of the technique of integration within Weyl ordered product of operators, i.e., the Weyl correspondence rule can be reconstructed by classical functions' Fourier transformation followed by an inverse Fourier transformation within Weyl ordering of operators. As an application of this reconstruction, we derive the quantum operator coresponding to the angular spectrum amplitude of a spherical wave.     

拓扑Weyl半金属简介

材料体系的拓扑量子行为是当前凝聚态物理研究的热点。作为一种新型拓扑量子态,Weyl半金属最近引起了人们的关注。文章以烧绿石结构铱氧化物A₂Ir₂O₇(其中A=Y或稀土元素)为例,介绍了Weyl半金属的奇特性质：Weyl点受拓扑保护稳定;Weyl半金属有着受拓扑保护的表面态,即非闭合的费米弧;Weyl半金属的反常霍尔效应与Weyl点的位置有关,和能带的细节无关;Weyl半金属特有的输运性质。文章还介绍了人们预言的几种Weyl半金属以及相关的实验进展。     

光晶格原子钟研究进展

钟跃迁频率在光学频段的光晶格原子钟已经实现了10-19 量级的频率稳定度和10-18 量级的频率不确定度, 在量子频标、 量子模拟和精密测量等领域有着重要的应用. 本文综述了光晶格原子钟的发展历史、 工作原理、 性能评估和应用与展望.     

Clocks and the Equivalence Principle

Einsteins equivalence principle has a number of problems, and it is often applied incorrectly. Clocks on the earth do not seem to be affected by the suns gravitational potential. The most commonly accepted reason given is a faulty application of the equivalence principle. While no valid reason is available within either the special or general theories of relativity, ether theories can provide a valid explanation. A clock bias of the correct magnitude and position dependence can convert the Selleri transformation of ether theories into an apparent Lorentz transformation, which gives rise to an apparent equivalence of inertial frames. The results indicate that the special theory is invalid and that only an apparent relativity exists.     

Conformal invariance in Weyl gravity

A conformal-invariant model of Weyl gravity, based on a nondecomposable representation of the conformal group, allows one to have a conformal-invariant propagator in an arbitrary gauge, as well as a conformal-invariant gauge-fixing term in the Lagrangian approach. It is shown that in the gauge-invariant sector this theory coincides with ordinary Weyl gravity (with conformal-noninvariant gauge fixing). The corresponding BRST transformations are found and are used for derivation of the Slavnov-Taylor identities.     

Weyl transformation in Fermi systems

In the path integral representation, the Hamiltonian in a quantum system is associated with the Hamiltonian in a classical system through the Weyl transformation. From this, it is possible to describe the time evolution in a quantum system by the Hamiltonian in a classical system. In a Bose system, the Weyl transformation is defined by the eigenstates of the canonical operators, since the Hamiltonian is given by a function of the canonical operators. On the other hand, in a Fermi system, the Hamiltonian is usually described by a function of the creation and annihilation operators, and hence the Weyl transformation is defined by the coherent states which are the eigenstate of an annihilation operator. Here, we formulate the Weyl transformation in Fermi systems in terms of the eigenstates of the canonical operators so as to clarify the correspondence between both systems. Using this, we can derive the path integral representation in Fermi systems.     

Charge transport in Weyl semimetals

We study transport in Weyl semimetals with N isotropic Weyl nodes in the presence of Coulomb interactions or disorder at temperature T. In the interacting clean limit, we determine the conductivity σ(ω,T) by solving a quantum Boltzmann equation within a "leading log" approximation and find it to be proportional to T, up to logarithmic factors arising from the flow of couplings. In the noninteracting disordered case, we compute the Kubo conductivity and show that it behaves differently for ω < T and ω > T: in the former regime we recover a previous result, of a finite dc conductivity and a Drude width vanishing as NT(2); in the latter, we find that σ(ω,T) vanishes linearly with ω with a leading term as T → 0 equal to the clean, free-fermion result: σ(0)((N))(ω,T = 0) = Ne(2)/12h|ω|/v(F). We compare our results to transport data on Y(2)Ir(2)O(7) and comment on the possible relevance to recent experiments on Eu(2)Ir(2)O(7).     

Weyl anomaly in two-dimensional supergravity

Two-dimensional supergravity theory is analyzed in terms of Weyl group cohomologies. A covariant nonlocal expression for the effective action is constructed. As in the case of ordinary gravity, its basic nonlocal part is determined by the well-known Polyakov action R1/□R.     

Singularities in Weyl gravitational fields

The peculiarities of the scalarS ≡R _ijkl R ^ijkl are exhibited for two axially-symmetric static (Weyl) gravitational fields. By examiningS along curved families of trajectories to the Weyl singularities, examples are found which contradict previous claims by Gautreau and Anderson regarding ‘directional singularities’. Proper circumferences about the Bach and Weyl line-mass singularity are also examined. There is no apparent correlation between the source structure and the behaviour ofS from this analysis.