Nucleon internal structure: a new set of quark, gluon momentum, angular momentum operators and parton distribution functions

It is unavoidable to deal with the quark and gluon momentum and angular momentum contributions to the nucleon momentum and spin in the study of nucleon internal structure. However we never have the quark and gluon momentum, orbital angular momentum and gluon spin operators which satisfy both the gauge invariance and the canonical momentum and angular momentum commutation relation. The conflicts between the gauge invariance and canonical quantization requirement of these operators are discussed. A new set of quark and gluon momentum, orbital angular momentum and spin operators, which satisfy both the gauge invariance and canonical momentum and angular momentum commutation relation, are proposed. The key point to achieve such a proper decomposition is to separate the gauge field into the pure gauge and the gauge covariant parts. The same conflicts also exist in QED and quantum mechanics and have been solved in the same manner. The impacts of this new decomposition to the nucleon internal structure are discussed.     

Energy–momentum tensor for the electromagnetic field in a dielectric

The total momentum of a thermodynamically closed system is unique, as is the total energy. Nevertheless, there is continuing confusion concerning the correct form of the momentum and the energy–momentum tensor for an electromagnetic field interacting with a linear dielectric medium. Rather than construct a total momentum from the Abraham momentum or the Minkowski momentum, we define a thermodynamically closed system consisting of a propagating electromagnetic field and a negligibly reflecting dielectric and we identify the Gordon momentum as the conserved total momentum by the fact that it is invariant in time. In the formalism of classical continuum electrodynamics, the Gordon momentum is therefore the unique representation of the total momentum in terms of the macroscopic electromagnetic fields and the macroscopic refractive index that characterizes the material. We also construct continuity equations for the energy and the Gordon momentum, noting that a time variable transformation is necessary to write the continuity equations in terms of the densities of conserved quantities. Finally, we use the continuity equations and the time–coordinate transformation to construct an array that has the properties of a traceless, symmetric energy–momentum tensor.     

Electromagnetic momentum conservation in media

That static electric and magnetic fields can store momentum may be perplexing, but is necessary to ensure total conservation of momentum. Simple situations in which such field momentum is transferred to nearby bodies and point charges have often been considered for pedagogical purposes, normally assuming vacuum surroundings. If dielectric media are involved, however, the analysis becomes more delicate, not least since one encounters the electromagnetic energy–momentum problem in matter, the ‘Abraham–Minkowski enigma’, of what the momentum is of a photon in matter. We analyze the momentum balance in three nontrivial examples obeying azimuthal symmetry, showing how the momentum conservation is satisfied as the magnetic field decays and momentum is transferred to bodies present. In the last of the examples, that of point charge outside a dielectric sphere in an infinite magnetic field, we find that not all of the field momentum is transferred to the nearby bodies; a part of the momentum appears to vanish as momentum flux towards infinity. We discuss this and other surprising observations which can be attributed to the assumption of magnetic fields of infinite extent. We emphasize how formal arguments of conserved quantities cannot determine which energy–momentum tensor is more “correct”, and each of our conservation checks may be performed equally well in the Minkowski or Abraham framework.     

Energy and angular momentum transfers from an electromagnetic wave to a copper ring in the UHF band

Electromagnetic waves could carry orbital angular momentum. Such momentum can be transferred to macroscopic objects and can make them rotate under a constant torque. Based on experimental observations, we investigate the origin of orbital angular momentum and energy transfer. Due to angular momentum and energy conservation, we show that angular momentum transfer is due to the change in the sign of angular momentum upon reflection. This leads to a rotational Doppler shift of the electromagnetic wave frequency, ensuring energy conservation.     

柱矢量光束的角动量性质

介绍了非近轴光束的表示理论,利用该表示理论很好地解决了非近轴光束的角动量问题,发现非近轴光束的总角动量可以严格地分解成自旋和轨道两部分,但是两者都依赖于由偏振椭圆度表征的光束的偏振状态。主要研究了柱矢量光束的角动量问题。给出了动量空间和位形空间中的柱矢量光束表达式和角动量算符表达式。通过分析两个空间中的角动量算符及柱矢量光束表达式,发现在这两种空间中,具有螺旋型相位的柱矢量光束是角动量算符沿着传播方向的分量的本征态,其本征值与偏振椭圆度无关,这为计算这类特殊光束的角动量提供了一种新方法。     

碘甲烷分子内层轨道的电子动量谱学研究

本文利用电子动量谱仪在1200 eV电子碰撞能量下测量了碘甲烷分子内层轨道电子束缚能谱和电子动量分布. 在能谱上观测到自旋-轨道耦合作用导致的两个分裂峰,得到了它们对应的电子动量分布. 采用相对论密度泛函理论方法计算了自旋-轨道分裂成分的电子动量分布,计算结果在电子动量大于1.0 a.u.区域内与实验测量符合很好,但在动量小于1.0 a.u.区域内严重低估了实验. 扭曲波理论计算很好地解释了低动量区的实验结果.     

Momentum,angular momentum,and equations of motion for test bodies in space-time with torsion

The definitions and transformation properties of momentum and angular momentum of test bodies possessing both macroscopic rotation and net spin are discussed. The equations of motion for momentum and angular momentum of test bodies are derived and written in a covariant form when the energy-momentum tensor is symmetric.     

On the gravitational angular momentum of rotating sources

The gravitational energy–momentum and angular momentum satisfy the algebra of the Poincaré group in the full phase space of the teleparallel equivalent of general relativity. The expression for the gravitational energy–momentum may be written as a surface integral in the three-dimensional spacelike hypersurface, whereas the definition for the angular momentum is given by a volume integral. It turns out that in practical calculations of the angular momentum of the gravitational field generated by localized sources like rotating neutron stars, the volume integral reduces to a surface integral, and the calculations can be easily carried out. Similar to previous investigations in the literature, we show that the total angular momentum is finite provided a certain asymptotic behaviour is verified. We discuss the dependence of the gravitational angular momentum on the frame, and argue that it is a measure of the dragging of inertial frames.     

Division of the energy and of the momentum of electromagnetic waves in linear media into electromagnetic and material parts

We defend a natural division of the energy density, energy flux and momentum density of electromagnetic waves in linear media in electromagnetic and material parts. In this division, the electromagnetic part of these quantities have the same form as in vacuum when written in terms of the macroscopic electric and magnetic fields, the material momentum is calculated directly from the Lorentz force that acts on the charges of the medium, the material energy is the sum of the kinetic and potential energies of the charges of the medium and the material energy flux results from the interaction of the electric field with the magnetized medium. We present reasonable models for linear dispersive non-absorptive dielectric and magnetic media that agree with this division. We also argue that the electromagnetic momentum of our division can be associated with the electromagnetic relativistic momentum, inspired on the recent work of Barnett [Phys. Rev. Lett. 104 (2010) 070401] that showed that the Abraham momentum is associated with the kinetic momentum and the Minkowski momentum is associated with the canonical momentum.     

INTERACTION BETWEEN A MOVING ATOM AND AN ELECTROMAGNETIC WAVE

Dynamics of a two-level atom moving in an electromagnetic field is studied. The atomic motion gives rise to a momentum-dependent detuning which holds back the atomic transition, and leads to a momentum-dependent Rabi oscillation which causes an overlapping among different Rabi oscillations. When the field is in a Fock state, the atomic population and the mean momentum of the atom exhibit damping oscillation, the damping rate is related to the momentum distribution; the collapse-revival phenomena of the atomic population and the mean momentum will occur if the atomic momentum has some special distribution. When the field is in a superposition state, the collapse-revival phenomena are modified by the atomic momentum distribution and disappear for the wider atomic momentum wavepackets. We also find that each atomic level will split into two sublevels with the same energy difference when the field is in a Fock state and the atom has a definite momentum.     

The ideal relativistic spinning gas: Polarization and spectra

We study the physics of the ideal relativistic rotating gas at thermodynamical equilibrium and provide analytical expressions of the momentum spectra and polarization vector for the case of massive particles with spin 1/2 and 1. We show that the finite angular momentum J entails an anisotropy in momentum spectra, with particles emitted orthogonally to J having, on average, a larger momentum than along its direction. Unlike in the non-relativistic case, the proper polarization vector turns out not to be aligned with the total angular momentum with a non-trivial momentum dependence.     

Angular momentum distribution in strong-field frustrated tunneling ionization

Using the classical-trajectory Monte Carlo model, we have theoretically studied the angular momentum distribution of frustrated tunneling ionization(FTI) of atoms in strong laser fields. Our results show that the angular momentum distribution of the FTI events exhibits a double-hump structure. With this classical model, we back traced the tunneling coordinates, i.e., the tunneling time and initial transverse momentum at tunneling ionization. It is shown that for the events tunneling ionized at the rising edge of the electric field,the final angular momentum exhibits a strong dependence on the initial transverse momentum at tunneling.While for the events ionized at the falling edge, there is a relatively harder recollision between the returning electron and the parent ion, leading to the angular momentum losing the correlation with the initial transverse momentum. Our study suggests that the angular momentum of the FTI events could be manipulated by controlling the initial coordinates of the tunneling ionization.     

Spin transport in the XXZ chain at finite temperature and momentum

We investigate the role of momentum for the transport of magnetization in the spin-1/2 Heisenberg chain above the isotropic point at finite temperature and momentum. Using numerical and analytical approaches, we analyze the autocorrelations of density and current and observe a finite region of the Brillouin zone with diffusive dynamics below a cutoff momentum, and a diffusion constant independent of momentum and time, which scales inversely with anisotropy. Lowering the temperature over a wide range, starting from infinity, the diffusion constant is found to increase strongly while the cutoff momentum for diffusion decreases. Above the cutoff momentum diffusion breaks down completely.     

Intrinsic and extrinsic nature of the orbital angular momentum of a light beam

We explain that, unlike the spin angular momentum of a light beam which is always intrinsic, the orbital angular momentum may be either extrinsic or intrinsic. Numerical calculations of both spin and orbital angular momentum are confirmed by means of experiments with particles trapped off axis in optical tweezers, where the size of the particle means it interacts with only a fraction of the beam profile. Orbital angular momentum is intrinsic only when the interaction with matter is about an axis where there is no net transverse momentum.     

Wigner Distributions in Light-Front Quark Models

We discuss the quark Wigner distributions which represent the quantum-mechanical analogues of the classical phase-space distributions. These functions can be obtained through a Fourier transform in the transverse space of the generalized transverse momentum dependent parton distributions, which encode the most general one-body information of partons in momentum space. In particular, we present a study within light-front quark models. The quark orbital angular momentum is also obtained from the phase-space average of the orbital angular momentum operator weighted with the Wigner distribution of unpolarized quark in a longitudinally polarized nucleon. The corresponding results calculated within different light-front quark models are compared with alternative definitions of the quark orbital angular momentum as given in terms of generalized parton distributions and transverse momentum dependent parton distributions.     

Electromagnetic momenta and forces in dispersive dielectric media

When the effects of dispersion are included, neither the Abraham nor the Minkowski expression for electromagnetic momentum in a dielectric medium gives the correct recoil momentum for absorbers or emitters of radiation. The total momentum density associated with a field in a dielectric medium has three contributions: (i) the Abraham momentum density of the field, (ii) the momentum density associated with the Abraham force, and (iii) a momentum density arising from the dispersive part of the response of the medium to the field, the latter having a form evidently first derived by Nelson (1991) [8]. All three contributions are required for momentum conservation in the recoil of an absorber or emitter in a dielectric medium. We consider the momentum exchanged and the force on a polarizable particle (e.g., an atom or a small dielectric sphere) in a host dielectric when a pulse of light is incident upon it, including the dispersion of the dielectric medium as well as a dispersive component in the response of the particle to the field. The force can be greatly increased in slow-light dielectric media.     

Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner

We use a Laguerre-Gaussian laser mode within an optical tweezers arrangement to demonstrate the transfer of the orbital angular momentum of a laser mode to a trapped particle. The particle is optically confined in three dimensions and can be made to rotate; thus the apparatus is an optical spanner. We show that the spin angular momentum of +/-?per photon associated with circularly polarized light can add to, or subtract from, the orbital angular momentum to give a total angular momentum. The observed cancellation of the spin and orbital angular momentum shows that, as predicted, a Laguerre-Gaussian mode with an azimuthal mode index l=1 has a well-defined orbital angular momentum corresponding to ? per photon.     

三维各向同性谐振子的几何动量分布

尽管几何动量最初的引入是为了描述超面上的运动粒子的动量,却不需要限制在真实的曲面上.如果一个曲线坐标系包含了超面族和超面上的法向矢量作为一个坐标轴的单位矢量,几何动量可以定义在超面族上,并参与构造对易力学量完全集.在三维各向同性谐振子中,采用球坐标描述,存在等效球面,并在球面族上建立对易力学量完全集.因此,三维各向同性谐振子同时具有动量和几何动量分布.这两个动量的差,可以定义为径向动量,从而使得径向动量可以测量.那么,通过几何动量,可以显示出狄拉克引进的径向动量的物理意义,而不是一直认为的那样完全不具有观测意义.     

用于微型卫星姿态控制的高温超导动量轮

卫星或宇宙飞船在太空中需要精确定位,动量轮是卫星或宇宙飞船姿态控制的关键部件.每个宇宙飞船上有三个或四个动量轮,这些动量轮虽然体积小,但是其角动量占宇宙飞船总角动量的绝大部分.动量轮实质上就是电机的转子,它具有很高的转动惯量.在适当的时间,启动或停止三个电机就能够控制宇宙飞船的姿态.我们已经研制了一个小的动量轮模型,该模型重量轻、结构紧凑,而且能效高.动量轮模型的主要创新点是使用了高温超导磁悬浮轴承,因此,它具有摩擦力小,转速高,储存动量大的特点.动量轮模型的最大设计转速为15,000RPM,储存的角动量为3.5J*s-1.     

On the momentum correlations in the fragmentation of <Superscript>197</Superscript>Au + <Superscript>197</Superscript>Au reactions

We aim to present the formation of fragments using static as well as momentum-dependent interactions and larger nucleonic cross-sections. We shall also examine, in detail, the role of momentum correlations in these situations which are close to the fire-ball as well as to the spectator matter decay. The role of momentum correlations will be studied by imposing an additional cut in the momentum space. A clear need of a momentum cut is demonstrated in both fire-ball as well as spectator matter physics. The momentum-dependent interactions and larger cross-sections play a drastic role in peripheral reactions, whereas the role of momentum cut remains the same in these situations.