scholarly journals Gauge invariant gluon spin operator for spinless nonlinear wave solutions

2017 ◽  
Vol 32 (11) ◽  
pp. 1750062 ◽  
Author(s):  
Bum-Hoon Lee ◽  
Youngman Kim ◽  
D. G. Pak ◽  
Takuya Tsukioka ◽  
P. M. Zhang
Keyword(s):  
Spin Density ◽  
Nonlinear Wave ◽  
Density Operator ◽  
Scale Parameter ◽  
Mass Scale ◽  
Wave Type ◽  
Gauge Invariant ◽  
Gluon Spin ◽  
Definition Of ◽  
Invariant Definition

We consider nonlinear 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 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 nonlinear wave type solutions have common features: presence of the mass scale parameter, nonvanishing 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 is 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.

scholarly journals Gauge invariant definition of the jet quenching parameter

2013 ◽  
Vol 2013 (2) ◽  
Author(s):  
Michael Benzke ◽  
Nora Brambilla ◽  
Miguel A. Escobedo ◽  
Antonio Vairo
Keyword(s):  
Jet Quenching ◽  
Gauge Invariant ◽  
Definition Of ◽  
Invariant Definition

scholarly journals PHYSICS OF GLUON HELICITY

2014 ◽  
Vol 25 ◽  
pp. 1460028
Author(s):  
XIANGDONG JI ◽  
YONG ZHAO
Keyword(s):  
Matrix Element ◽  
Time Correlation ◽  
Spin Operator ◽  
Large Momentum ◽  
Time Correlation Functions ◽  
Gauge Invariant ◽  
Equal Time ◽  
Polarized Proton ◽  
Gluon Spin ◽  
Gluon Helicity

The total gluon helicity in a polarized proton is shown to be a matrix element of a gauge-invariant but nonlocal, frame-dependent gluon spin operator [Formula: see text] in the large momentum limit. The operator [Formula: see text] is fit for the calculation of the total gluon helicity in lattice QCD. This calculation also implies that parton physics can be studied through the large momentum limit of frame-dependent, equal-time correlation functions of quarks and gluons.

Energy Content Characterization of Water Waves Using Linear and Nonlinear Spectral Analysis

2021 ◽  
pp. 1-30
Author(s):  
Ali Mohtat ◽  
Solomon Yim ◽  
Alfred R. Osborne
Keyword(s):  
Wave Field ◽  
Nonlinear Wave ◽  
Water Waves ◽  
Ad Hoc ◽  
Energy Content ◽  
Energy Calculation ◽  
Linear And Nonlinear ◽  
Definition Of ◽  
Exact Energy ◽  
Wave Modes

Abstract The survivability, safe operation, and design of marine vehicles and wave energy converters are highly dependent on accurate characterization and estimation of the energy content of the ocean wave field. In this study, analytical solutions of the nonlinear Schrödinger equation (NLS) using periodic inverse scattering transformation (IST) and its associated Riemann spectrum are employed to obtain the nonlinear wave modes (eigen functions of the nonlinear equation consisting of multiple phase-locked harmonic components). These nonlinear wave modes are used in two approaches to develop a more accurate definition of the energy content. First, in an ad hoc approach, the amplitudes of the nonlinear wave modes are used with a linear energy calculation resulting in a semi-linear energy estimate. Next, a novel, mathematically exact definition of the energy content taking into account the nonlinear effects up to fifth order is introduced in combination with the nonlinear wave modes, the exact energy content of the wave field is computed. Experimental results and numerical simulations were used to compute and analyze the linear, ad hoc, and exact energy contents of the wave field, using both linear and nonlinear spectra. The ratio of the ad hoc and exact energy estimates to the linear energy content were computed to examine the effect of nonlinearity on the energy content. In general, an increasing energy ratio was observed for increasing nonlinearity of the wave field, with larger contributions from higher-order harmonic terms. It was confirmed that the significant increase in nonlinear energy content with respect to its linear counterpart is due to the increase in the number of nonlinear phase-locked (bound wave) modes.

scholarly journals Renormalon-free definition of the gluon condensate within the large-$\beta_0$ approximation

2019 ◽  
Vol 2019 (10) ◽  
Author(s):  
Hiroshi Suzuki ◽  
Hiromasa Takaura
Keyword(s):  
Operator Product Expansion ◽  
Density Operator ◽  
Gradient Flow ◽  
Gluon Condensate ◽  
Operator Product ◽  
Clear Definition ◽  
Lattice Data ◽  
Perturbative Calculation ◽  
Yang Mills ◽  
Definition Of

Abstract We propose a clear definition of the gluon condensate within the large-$\beta_0$ approximation as an attempt toward a systematic argument on the gluon condensate. We define the gluon condensate such that it is free from a renormalon uncertainty, consistent with the renormalization scale independence of each term of the operator product expansion (OPE), and an identical object irrespective of observables. The renormalon uncertainty of $\mathcal{O}(\Lambda^4)$, which renders the gluon condensate ambiguous, is separated from a perturbative calculation by using a recently suggested analytic formulation. The renormalon uncertainty is absorbed into the gluon condensate in the OPE, which makes the gluon condensate free from the renormalon uncertainty. As a result, we can define the OPE in a renormalon-free way. Based on this renormalon-free OPE formula, we discuss numerical extraction of the gluon condensate using the lattice data of the energy density operator defined by the Yang–Mills gradient flow.

New exact solutions of nonlinear wave type PDEs with delay

2020 ◽  
Vol 108 ◽  
pp. 106512 ◽  
Author(s):  
Andrei D. Polyanin ◽  
Vsevolod G. Sorokin
Keyword(s):  
Exact Solutions ◽  
Nonlinear Wave ◽  
Wave Type ◽  
New Exact Solutions
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