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.     

Minimum uncertainty states in angular momentum and angle variables for charged particles in structured electromagnetic fields

We study the phase-space properties of a charged particle in a static electromagnetic field exhibiting vortex pairs with complementary topological charges and in a pure gauge field. A stationary solution of the Schrödinger equation that minimizes the uncertainty relations for angular momentum and trigonometric functions of the phase is obtained. It does not exhibit vortices and the angular momentum is due to the gauge field only. Increasing the topological charge of the vortices increases the regions where the Wigner function in the angle–angular momentum plane takes negative values, and thus enhances the quantum character of the dynamics.     

Time-resolved phase-space distributions for light backscattered from a disordered medium

We demonstrate time-resolved measurement of optical phase-space distributions as a new probe for investigating the propagation of light in disordered media. Phase-space techniques measure the joint transverse position and momentum distribution of the scattered light, and are sensitive to the spatially varying phase and amplitude of the field. Using this method we investigate light backscattered from a random medium. The measurements indicate that the weakly localized component is a phase conjugate of the incident light field. A new model of backscatter, based on Wigner phase-space distributions, elucidates the spatial and angular behavior of the localized and unlocalized components.     

Global Symmetry in Phase-Space Path Integral for a System With a Singular Lagrangian

Based on the phase-space generating functional of a system with a singular Lagrangion,the Ward identities under global transformation in phase are deduced.The quantum conservation laws under the global symmetry transiormation are also derived which is in general different from classical Hoether's ones.The preliminary application of our formulation to the Yang-Mills theory the Ward-Takahashi identity and BRS conserved quantity for BRS transformation are presented.Applying to non-Abelian-Chern-Simons theory the quantum conserved angular momentum (QCAM) are obtained.The QCAM differs form classical one because the former needs to take into account the distribution of angular momentum of ghost innon-Abelian-Chern-Simons theory.     

Canonical Symmetries in the Functional Formalism

Based on the phase-space generating functionalof the Green function, the canonical Ward identities(CWI) under local, nonlocal, and global transformationsin phase space for a system with a regular and singular Lagrangian have been derived. Therelation of global canonical symmetries to conservationlaws at the quantum level is presented. The advantage ofthis formulation is that one does not need to carry out the integration over canonicalmomenta in a phase-space path (functional) integral asin the traditional treatment in configuration space. Ingeneral, the connection between global canonicalsymmetries and conservation laws in classical theories isno longer preserved in quantum theories. Applications ofour formulation to the non-Abelian Chern-Simons (CS)theory are given, and new forms for CS gauge-ghost field proper vertices and the quantal conservedangular momentum of this system are obtained; thisangular momentum differs from the classical one in thatone needs to take into account the contribution of angular momenta of ghost fields.     

On phase-space representations of quantum mechanics using Glauber coherent states

A phase-space formulation of quantum mechanics is proposed by constructing two representations (identified as pq and qp) in terms of the Glauber coherent states, in which phase-space wave functions (probability amplitudes) play the central role, and position q and momentum p are treated on equal footing. After finding some basic properties of the pq and qp wave functions, the quantum operators in phase-space are represented by differential operators, and the Schrödinger equation is formulated in both pictures. Afterwards, the method is generalized to work with the density operator by converting the quantum Liouville equation into pq and qp equations of motion for two-point functions in phase-space. A coordinate transformation between those points allows one to construct a cell in phase-space, whose central point can be treated as a parameter. In this way, one gets equations of motion describing the evolution of one-point functions in phase-space. Finally, it is shown that some quantities obtained in this paper are related in a natural way with cross-Wigner functions, which are constructed with either the position or the momentum wave functions.     

含Chern-Simons项的旋量电动力学的量子正则对称性

构造了含Chern-Simons(CS)项的旋量电动力学的规范变换生成元.按约束Hamilton系统的Faddeev-Senjanovic(FS)路径积分量子化方案,给出了该系统Green函数的相空间生成泛函;导出了正则Ward恒等式;分析了系统的量子守恒角动量,指出它具有分数自旋性质.     

Quantal Canonical Symmetries in Spinor QED with Chern-Simons Term

The generator of gauge transformation for spinor QED with Chern-Simons (CS) term has been constructed. According to the rule of path integral quantization for constrained system in Faddeev-Senjanovic scheme, the phase-space generating of Green function is obtained, and canonical Ward identities for such a system is also derived. The quantal conserved angular momentum for spinor QED with CS term is studied. The property of fractional spin of the system is pointed out.     

Topological Chern—Simons vortices in the O (3) σ -model

Based on the phase-space path integral (functional integral) for a system with a regular or singular Lagrangian, the generalized Ward identities for phase space generating functional under the global transformation in phase space are derived respectively. The canonical Noether theorem at the quantum level is also established. It is pointed out that the connection between the symmetries and conservation laws in classical theories, in general,is no longer preserved in quantum theories. The advantage of our formulation is that we do not need to carry out the integration over the canonical momenta as usually performed. Applying the present formulation to Yang-Mills theory, the quantal BRS conserved quantity and Ward-Takahashi identity for BRS tranformation are derived; the Ward identities for gaugeghost proper vertices and new quantal conserved quantity are also found. In comparison of quantal conservation laws with those one deriving from configuration-space path integral using the Faddeev-Popov(F-P) trick is discussed. A precise study of path-integral quantisation for a nonlinear sigma model with Hopf and Chern-Simons (CS) terms is reexamined. It has been shown that the angular momentum at the quantum level is equal to classical (Noether ) one. Applying our formulation to non-Abelian CS theory, the quantal conserved angular momentum of this system is obtained which differs from classical one in that one needs to take into account the contribution of angular momenta of ghost fields.     

A semi-classical description of nuclear phase-space and momentum distributions in hot nuclei

The nuclear phase-space distribution is calculated in a semi-classical approximation using the inverse Laplace transformation of the Bloch density. For a local Woods-Saxon potential, both the phase-space and the momentum distributions are shown as functions of the temperature.     

Orbital angular momentum exchange in the interaction of twisted light with molecules

In the interaction of molecules with light endowed with orbital angular momentum, an exchange of orbital angular momentum in an electric dipole transition occurs only between the light and the center of mass motion; i.e., internal "electronic-type" motion does not participate in any exchange of orbital angular momentum in a dipole transition. A quadrupole transition is the lowest electric multipolar process in which an exchange of orbital angular momentum can occur between the light, the internal motion, and the center of mass motion. This rules out experiments seeking to observe exchange of orbital angular momentum between light beams and the internal motion in electric dipole transitions.     

Binary-black-hole encounters, gravitational bursts, and maximum final spin

The spin of the final black hole in the coalescence of nonspinning black holes is determined by the "residual" orbital angular momentum of the binary. This residual momentum consists of the orbital angular momentum that the binary is not able to shed in the process of merging. We study the angular momentum radiated, the spin of the final black hole, and the gravitational bursts in a sequence of equal mass encounters. The initial orbital configurations range from those producing an almost direct infall to others leading to numerous orbits before infall, with multiple bursts of radiation. Our sequence consists of orbits with fixed impact parameter. What varies is the initial linear momentum of the black holes. For this sequence, the final black hole of mass M_{h} gets a maximum spin parameter a/M_{h} approximately 0.823, with this maximum occurring for initial orbital angular momentum L/M_{h};{2} approximately 1.176.     

The angular momentum of light: optical spanners and the rotational frequency shift

An introduction is given to the concepts of the spin and orbital angular momentum of light beams. Both spin and orbital angular momentum can be transferred from a light beam to particles held within optical tweezers, so forming an optical spanner. Each also give rise to a frequency shift when the light beam is rotated. This arises because quarter or half-wave plates and /2 or mode converters play equivalent roles for spin and orbital angular momentum respectively.     

Bimodality as a signal of a liquid-gas phase transition in nuclei?

We use the heavy-ion phase-space exploration model to discuss the origin of the bimodality in charge asymmetry observed in nuclear reactions around the Fermi energy. We show that it may be related to the important angular momentum (spin) transferred into the quasiprojectile before secondary decay. As the spin overcomes the critical value, a sudden opening of decay channels is induced and leads to a bimodal distribution for the charge asymmetry. In the model, it is not assigned to a liquid-gas phase transition but to specific instabilities in nuclei with high spin. Therefore, we propose to use these reactions to study instabilities in rotating nuclear droplets.     

State change, quantum probability, and information in operational phase-space measurement

State change, quantum probability, and information gain in the operational phasespace measurement are formulated by means of positive operator-valued measure (POVM) and operation. The properties of the operational POVM and its marginal POVM which yield the quantum probability distributions of the measurement outcomes obtained by the operational phase-space measurement are investigated. The Naimark extension of the operational POVM can be expressed in terms of the relative-position states and the relative-momentum states in the extended Hilbert space. An observable quantity measured in the operational phase-space measurement becomes a fuzzy or unsharp observable. The state change of a physical system caused by the operational phase-space measurement is described by the operation which is obtained explicitly for the position and momentum measurements and for the simultaneous measurement of position and momentum. Using the results, the entropy change of the measured physical system and the information gain in the operational phase-space measurement are investigated. It is found that the average value of the entropy change is equal to the Shannon mutual information extracted from the outcomes exhibited by the measurement apparatus.     

The effect of alignment of the exotic atom orbital angular momentum on depolarization of negative muons

The theory of cascade depolarization of negative muons is generalized to the case where the orbital angular momentum of a meson becomes aligned as a result of its atomic capture. An explanation of the experimental data on the residual polarization of ^– in helium is proposed on the basis of the developed theory and available arguments in favour of the possible existence of alignment of the orbital angular momentum in the lightes exotic atoms. An angular distribution and linear polarization of muonic X-rays is considered. The connection between these characteristics and the depolarization factor due to the alignment of the orbital angular momentum enables one to make a direct experimental test of the proposed explanation of the residual polarization of muons in helium.     

Angular Momentum-Free of the Entropy Relations for Rotating Kaluza-Klein Black Holes

Based on a mathematical lemma related to the Vandermonde determinant and two theorems derived from the first law of black hole thermodynamics, we investigate the angular momentum independence of the entropy sum as well as the entropy product of general rotating Kaluza-Klein black holes in higher dimensions. We show that for both non-charged rotating Kaluza-Klein black holes and non-charged rotating Kaluza-Klein-AdS black holes, the angular momentum of the black holes will not be present in entropy sum relation in dimensions d≥4, while the independence of angular momentum of the entropy product holds provided that the black holes possess at least one zero rotation parameter a _j = 0 in higher dimensions d≥5, which means that the cosmological constant does not affect the angular momentum-free property of entropy sum and entropy product under the circumstances that charge δ=0. For the reason that the entropy relations of charged rotating Kaluza-Klein black holes as well as the non-charged rotating Kaluza-Klein black holes in asymptotically flat spacetime act the same way, it is found that the charge has no effect in the angular momentum-independence of entropy sum and product in asymptotically flat spactime.     

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.     

超导电子的角动量和磁通量子化

本文指出,磁通量子化应和超导电子的角动量量子化一致。分数角动量的存在必然导致分数磁通量子化,而分数磁通量子化和超导理论以及迄今为止的实验结果不相矛盾。我们提出和分析的一个新实验可以检测任意子和分数磁通量子。 关键词：