Hybrid multilane models for highway traffic

Zhang, Taiyi; Lin, Yueh-hsiang

doi:10.1140/epjb/e2018-90500-3

Cited by 7 publications

(9 citation statements)

References 27 publications

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“…This enables us to write down gaugeinvariant expression of the gluon spin as well as that of the g.i.c. OAM of quarks in the nucleon 30 [35], [36]. (More precisely, the gluon spin should be called the gluon helicity or the longitudinal component of the gluon spin with respect to the direction of the nucleon momentum.)…”

Section: Remarks On the Issue Of Gauge Choice In The Nucleon Spin Decmentioning

confidence: 99%

The issue of gauge choice in the Landau problem and the physics of canonical and mechanical orbital angular momenta

Wakamatsu¹,

Kitadono²,

Zhang³

2018

Annals of Physics

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One intriguing issue in the nucleon spin decomposition problem is the existence of two types of decompositions, which are representably characterized by two different orbital angular momenta (OAMs) of quarks. The one is the mechanical OAM, while the other is the so-called gauge-invariant canonical (g.i.c.) OAM, the concept of which was introduced by Chen et al. An especially delicate quantity is the g.i.c. OAM, which must be distinguished from the ordinary (gauge-variant) canonical OAM. We find that, owing to its analytically solvable nature, the famous Landau problem offers an ideal tool to understand the difference and the physical meaning of the above three OAMs, i.e. the standard canonical OAM, g.i.c. OAM, and the mechanical OAM. We analyze these three OAMs in two different formulations of the Landau problem, first in the standard (gauge-fixed) formulation and second in the gauge-invariant (but path-dependent) formulation of DeWitt. Especially interesting is the latter formalism. It is shown that the choice of path has an intimate connection with the choice of gauge, but they are not necessarily equivalent. Then, we answer the question about what is the consequence of a particular choice of path in DeWitt's formalism. This analysis also clarifies the implication of the gauge symmetry hidden in the concept of g.i.c. OAM. Finally, we show that the finding above offers a clear understanding about the uniqueness or non-uniqueness problem of the nucleon spin decomposition, which arises from the arbitrariness in the definition of the so-called physical component of the gauge field.

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Section: Remarks On the Issue Of Gauge Choice In The Nucleon Spin Decmentioning

confidence: 99%

The issue of gauge choice in the Landau problem and the physics of canonical and mechanical orbital angular momenta

Wakamatsu¹,

Kitadono²,

Zhang³

2018

Annals of Physics

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“…The meaning of the helicity conditions is simple, they fix pure gauge degrees of freedom while keeping two transverse dynamic degrees of freedom of the gluon. Generalization of such description of the helicity operator to the case of non-Abelian theory has been done in [35,36,39,40]. Since the helicity operator is Lorentz frame independent, all definitions satisfying the helicity conditions are consistent even though the defining equations for the physical gauge potential are not manifestly Lorentz invariant [5,40].…”

Section: Gluon Spin Density Operatormentioning

confidence: 99%

“…The Lorenz gauge type condition (38) was proposed in [37] as a transversality condition. In the case of Maxwell theory the definition of a gauge invariant photon spin operator based on the solution of the Lorenz type equation (38) encounters a well-known problem of incompleteness of the Lorenz gauge [40]. Namely, in the Lorenz gauge one has still a residual symmetry which implies that equation of motion for the temporal component of the gauge potential admits unphysical propagating modes.…”

Section: Gluon Spin Density Operatormentioning

confidence: 99%

“…Note that the solution (40) for the physical gauge potential includes an expressionÂ a long µ containing the longitudinal part, ∂ ρ A a ρ , of the unconstrained gauge potential. The fact that a gauge invariant expression (40) is given in terms of the gauge potential, not in terms of the field strength, reflects the property of the non-Abelian gauge theory where the field strength does not determine all gauge invariant quantities as it occurs in the Abelian gauge theory. One should stress that non-locality appearing in the solution for the physical gauge potential is unphysical.…”

Section: Gluon Spin Density Operatormentioning

confidence: 99%

“…Summarizing, we propose a new definition for the gluon spin operator for a class of non-linear plane wave solutions which admit a non-vanishing mass and a total spin zero. The definition for the physical gauge potential is based on the equation (38) and we have provided an explicit construction for the physical gauge potential, (40), which leads to unique gauge invariant and Lorentz frame independent definition of the gluon spin operator for massive spinless non-linear plane waves. Note, that equation (38) was suggested in [37] as a possible definition of the gluon spin operator for massless gluons with helicity ±1.…”

Section: Gluon Spin Density Operatormentioning

confidence: 99%

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Gauge invariant gluon spin operator for spinless nonlinear wave solutions

Lee

Kim

Pak

et al. 2017

Int. J. Mod. Phys. A

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We consider non-linear wave type solutions with intrinsic mass scale parameter and zero spin in a pure SU (2) quantum chromodynamics (QCD). A new stationary solution which can be treated as a system of a static Wu-Yang monopole dressed in off-diagonal gluon field is proposed. A remarkable feature of such a solution is that it possesses a finite energy density everywhere. All considered non-linear wave type solutions have common features: presence of the mass scale parameter, non-vanishing projection of the color fields along the propagation direction and zero spin. The last property requires revision of the gauge invariant definition of the spin density operator which supposed to produce spin one states for the massless vector gluon field. We construct a gauge invariant definition of the classical gluon spin density operator which is unique and Lorentz frame independent.

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