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Angular Momentum Operator

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C. Lorcé – One of the best experts on this subject based on the ideXlab platform.

  • Wigner Distributions in Light-Front Quark Models
    Few-Body Systems, 2014
    Co-Authors: B. Pasquini, C. Lorcé

    Abstract:

    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.

  • Quark orbital Angular Momentum from Wigner distributions and light-cone wave functions
    Physical Review D, 2012
    Co-Authors: C. Lorcé, B. Pasquini, X. Xiong, F. Yuan

    Abstract:

    We investigate the quark orbital Angular Momentum of the nucleon in the absence of gauge-field degrees of freedom, by using the concept of the Wigner distribution and the light-cone wave functions of the Fock-state expansion of the nucleon. The quark orbital Angular Momentum is obtained from the phase-space average of the orbital Angular Momentum Operator weighted with the Wigner distribution of unpolarized quarks in a longitudinally polarized nucleon. We also derive the light-cone wave-function representation of the orbital Angular Momentum. In particular, we perform an expansion in the nucleon Fock-state space and decompose the orbital Angular Momentum into the N-parton state contributions. Explicit expressions are presented in terms of the light-cone wave functions of the three-quark Fock state. Numerical results for the up and down quark orbital Angular momenta of the proton are shown in the light-cone constituent quark model and the light-cone chiral quark-soliton model.

F. Yuan – One of the best experts on this subject based on the ideXlab platform.

  • Quark orbital Angular Momentum from Wigner distributions and light-cone wave functions
    Physical Review D, 2012
    Co-Authors: C. Lorcé, B. Pasquini, X. Xiong, F. Yuan

    Abstract:

    We investigate the quark orbital Angular Momentum of the nucleon in the absence of gauge-field degrees of freedom, by using the concept of the Wigner distribution and the light-cone wave functions of the Fock-state expansion of the nucleon. The quark orbital Angular Momentum is obtained from the phase-space average of the orbital Angular Momentum Operator weighted with the Wigner distribution of unpolarized quarks in a longitudinally polarized nucleon. We also derive the light-cone wave-function representation of the orbital Angular Momentum. In particular, we perform an expansion in the nucleon Fock-state space and decompose the orbital Angular Momentum into the N-parton state contributions. Explicit expressions are presented in terms of the light-cone wave functions of the three-quark Fock state. Numerical results for the up and down quark orbital Angular momenta of the proton are shown in the light-cone constituent quark model and the light-cone chiral quark-soliton model.

John C Light – One of the best experts on this subject based on the ideXlab platform.

  • symmetry adapted direct product discrete variable representation for the coupled Angular Momentum Operator application to the vibrations of co2 2
    Journal of Chemical Physics, 2003
    Co-Authors: H S Lee, Hua Chen, John C Light

    Abstract:

    The theoretical (quantum) description of large amplitude vibrations of systems containing four or more atoms using orthogonal internal coordinates requires three or more Angular coordinates. The basis commonly used to represent these coordinates is the coupled Angular Momentum basis. We show that a direct product Angular discrete variable representation (DVR) can be used advantageously, particularly for systems with high permutation-inversion symmetry and nonlinear equilibrium geometry. The DVR permits full symmetry projection and solution by the sequential diagonalization and truncation method. Application to the dimer of rigid CO2 demonstrates the accuracy and efficiency of the approach.

  • a grid representation for spherical angles decoupling of the Angular Momentum Operator
    Journal of Chemical Physics, 1997
    Co-Authors: Jiqiong Dai, John C Light

    Abstract:

    The Angular Momentum Operator which is a function of the orientational angle θ and the azimuthal angle φ may be split into the φ-dependent and φ-independent parts so that the split exponential Operator method can be exactly implemented (with orthogonal transformations) in a direct product discrete variable representation of θ and φ. Although one loses the exact representation of the Angular Momentum in the spherical harmonic basis, the direct product representations have been proved to converge and to be stable and efficient. An advantage is that computational time for a wave-packet propagation (for a matrix-vector product) is reduced for split exponential propagators since a direct product representation is preserved for all the angles.