scholarly journals Classical equation of motion and anomalous dimensions at leading order

2016 ◽  
Vol 2016 (7) ◽  
Author(s):  
Keita Nii
Keyword(s):  
Classical Equation ◽  
Equation Of Motion ◽  
Leading Order ◽  
Anomalous Dimensions

Coherent states, Schrödinger equation, and the Hamilton–Jacobi equation

1995 ◽  
Vol 73 (7-8) ◽  
pp. 478-483
Author(s):  
Rachad M. Shoucri
Keyword(s):  
Schrödinger Equation ◽  
Jacobi Equation ◽  
Coherent States ◽  
Schrodinger Equation ◽  
Hidden Variables ◽  
Classical Equation ◽  
Equation Of Motion ◽  
Phase Variable ◽  
Independent Variable ◽  
Hamilton Jacobi Equation

The self-adjoint form of the classical equation of motion of the harmonic oscillator is used to derive a Hamiltonian-like equation and the Schrödinger equation in quantum mechanics. A phase variable ϕ(t) instead of time t is used as an independent variable. It is shown that the Hamilton–Jacobi solution in this case is identical with the solution obtained from the Schrödinger equation without the need to introduce the idea of hidden variables or quantum potential.

A Covariant Semi-Classical Theory of the Radiating Electron

1977 ◽  
Vol 32 (1) ◽  
pp. 101-102
Author(s):  
M. Sorg
Keyword(s):  
Classical Theory ◽  
Characteristic Length ◽  
Order Approximation ◽  
Classical Equation ◽  
Radiation Reaction ◽  
Equation Of Motion ◽  
Compton Wavelength ◽  
Classical Electron ◽  
Electron Radius ◽  
Classical Electron Radius

Abstract A new semi-classical equation of motion is suggested for the radiating electron. The characteristic length of the new theory is the Compton wavelength λc(= ħ/2 m c) instead of the classical electron radius which is used in all purely classical theories of the radiating electron. However, the lowest order approximation of the radiation reaction contains only the classical radius rc.

Coherent states and geometric phases of a generalized damped harmonic oscillator with time-dependent mass and frequency

2014 ◽  
Vol 28 (26) ◽  
pp. 1450177 ◽  
Author(s):  
I. A. Pedrosa ◽  
D. A. P. de Lima
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Classical Equation ◽  
Equation Of Motion ◽  
Time Dependent ◽  
Quantum Invariant ◽  
Dynamical Phase ◽  
Special Cases ◽  
Berry Phases ◽  
Dependent Mass

In this paper, we study the generalized harmonic oscillator with arbitrary time-dependent mass and frequency subjected to a linear velocity-dependent frictional force from classical and quantum points of view. We obtain the solution of the classical equation of motion of this system for some particular cases and derive an equation of motion that describes three different systems. Furthermore, with the help of the quantum invariant method and using quadratic invariants we solve analytically and exactly the time-dependent Schrödinger equation for this system. Afterwards, we construct coherent states for the quantized system and employ them to investigate some of the system's quantum properties such as quantum fluctuations of the coordinate and the momentum as well as the corresponding uncertainty product. In addition, we derive the geometric, dynamical and Berry phases for this nonstationary system. Finally, we evaluate the dynamical and Berry phases for three special cases and surprisingly find identical expressions for the dynamical phase and the same formulae for the Berry's phase.

scholarly journals Drell-Yan angular lepton distributions at small x from TMD factorization.

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Ian Balitsky
Keyword(s):  
Transverse Momentum ◽  
Pair Production ◽  
Cross Section ◽  
Z Boson ◽  
Equation Of Motion ◽  
Leading Order ◽  
Small X ◽  
Mulders Function

Abstract The Drell-Yan process is studied in the framework of TMD factorization in the Sudakov region s » Q2 » $$ {q}_{\perp}^2 $$ q ⊥ 2 corresponding to recent LHC experiments with Q2 of order of mass of Z-boson and transverse momentum of DY pair ∼ few tens GeV. The DY hadronic tensors are expressed in terms of quark and quark-gluon TMDs with $$ \frac{1}{Q^2} $$ 1 Q 2 and $$ \frac{1}{N_c^2} $$ 1 N c 2 accuracy. It is demonstrated that in the leading order in Nc the higher-twist quark-quark-gluon TMDs reduce to leading-twist TMDs due to QCD equation of motion. The resulting hadronic tensors depend on two leading-twist TMDs: f1 responsible for total DY cross section, and Boer-Mulders function $$ {h}_1^{\perp } $$ h 1 ⊥ . The corresponding qualitative and semi-quantitative predictions seem to agree with LHC data on five angular coefficients A0− A4 of DY pair production. The remaining three coefficients A5− A7 are determined by quark-quark-gluon TMDs multiplied by extra $$ \frac{1}{N_c} $$ 1 N c so they appear to be relatively small in accordance with LHC results.

scholarly journals SUSY-like relation of the splitting functions in evolution of gluon and quark jet multiplicities

2018 ◽  
Vol 191 ◽  
pp. 04006
Author(s):  
Anatoly Kotikov
Keyword(s):  
Evolution Equations ◽  
Dglap Evolution ◽  
Leading Order ◽  
Logarithmic Order ◽  
World Data ◽  
Charged Hadrons ◽  
Anomalous Dimensions ◽  
The World ◽  
Fragmentation Functions ◽  
Gluon Fragmentation

We show the new relationship [1] between the anomalous dimensions, resummed through next-to-next-to-leading-logarithmic order, in the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations for the first Mellin moments Dq,g(μ2) of the quark and gluon fragmentation functions, which correspond to the average hadron multiplicities in jets initiated by quarks and gluons, respectively. So far, such relationships have only been known from supersymmetric (SUSY) QCD. Exploiting available next-to-nextto- next-to-leading-order (NNNLO) information on the ratio D+g (μ2)=D+q (μ2) of the dominant plus components, the fit of the world data of Dq,g(μ2) for charged hadrons measured in e+e- annihilation leads to α(5)s (MZ) = 0:1205 +0:0016 -0:0020.

QUANTUM BOUNCE OF A UNIFORM DUST STAR IN NEWTON GRAVITY

1991 ◽  
Vol 06 (10) ◽  
pp. 855-859 ◽  
Author(s):  
H. ISHIHARA ◽  
S. MORITA ◽  
H. SATO
Keyword(s):  
Wave Packet ◽  
Numerical Method ◽  
Quantum Dynamics ◽  
Classical Equation ◽  
Equation Of Motion ◽  
Quantum Systems ◽  
Newtonian Limit ◽  
Newtonian Gravity

We investigate the quantum dynamics of a dust sphere collapsing uniformly in Newtonian gravity, in which the concept of time is obvious. The quantum bounce of the wave packet is observed by a numerical method. Our Newton Lagrangian is different from the Newtonian limit of the Einstein Lagrangian. They give the same classical equation of motion but derive the different quantum systems.

Fuzzy Transitions from Quantum to Classical Mechanics and New Phenomena of Mesoscopic Objects

1997 ◽  
Vol 52 (1-2) ◽  
pp. 25-30
Author(s):  
J. P. Hsu
Keyword(s):  
Wave Equation ◽  
Classical Mechanics ◽  
Classical Equation ◽  
Experimental Tests ◽  
Equation Of Motion ◽  
Generalized Equation ◽  
Invariant Equation ◽  
Macroscopic Objects ◽  
New Phenomena ◽  
New Phase

Abstract A new "phase invariant" equation of motion for both microscopic and macroscopic objects is proposed. It reduces to the probabilistic wave equation for small masses and the deterministic classical equation for large masses. The motions of mesoscopic objects and fuzzy transitions between quantum and classical mechanics are discussed on the basis of the generalized equation. Experimental tests of new predictions are discussed.

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