scholarly journals Color Confinement and Spatial Dimensions in the Complex-Sedenion Space

2017 ◽  
Vol 2017 ◽  
pp. 1-26 ◽  
Author(s):  
Zi-Hua Weng
Keyword(s):  
Wave Function ◽  
Complex Number ◽  
Degrees Of Freedom ◽  
Unit Vector ◽  
Wave Functions ◽  
Field Equations ◽  
Abelian Gauge ◽  
Color Confinement ◽  
Complex Quaternion ◽  
Spatial Dimensions

The paper aims to apply the complex-sedenions to explore the wave functions and field equations of non-Abelian gauge fields, considering the spatial dimensions of a unit vector as the color degrees of freedom in the complex-quaternion wave functions, exploring the physical properties of the color confinement essentially. J. C. Maxwell was the first to employ the quaternions to study the electromagnetic fields. His method inspires subsequent scholars to introduce the quaternions, octonions, and sedenions to research the electromagnetic field, gravitational field, and nuclear field. The application of complex-sedenions is capable of depicting not only the field equations of classical mechanics, but also the field equations of quantum mechanics. The latter can be degenerated into the Dirac equation and Yang-Mills equation. In contrast to the complex-number wave function, the complex-quaternion wave function possesses three new degrees of freedom, that is, three color degrees of freedom. One complex-quaternion wave function is equivalent to three complex-number wave functions. It means that the three spatial dimensions of unit vector in the complex-quaternion wave function can be considered as the “three colors”; naturally the color confinement will be effective. In other words, in the complex-quaternion space, the “three colors” are only the spatial dimensions, rather than any property of physical substance.

Multiscalar field models: Interaction potentials, wave functions and cosmological solutions

2020 ◽  
Vol 29 (07) ◽  
pp. 2050046
Author(s):  
Sameerah Jamal
Keyword(s):  
Wave Function ◽  
Wave Functions ◽  
Scalar Interaction ◽  
Coordinate Transformations ◽  
Spatial Curvature ◽  
Field Equations ◽  
Interaction Potentials ◽  
Cosmological Solutions ◽  
The Universe ◽  
Friedmann Robertson Walker

We consider a multiscalar tensor cosmology model described by Friedmann–Robertson–Walker (FRW) spacetime with zero spatial curvature. Three specific scalar interaction potentials that characterize the model are analyzed under a set of coordinate transformations. By implication, we solve for the wave function of the universe, reduce the dimension of the underlying Hamiltonian system and consequently, establish analytical solutions of the multiscalar model’s field equations.

Topology of QCD vacuum and color confinement

2002 ◽  
Vol 80 (7) ◽  
pp. 745-754 ◽  
Author(s):  
H C Chandola ◽  
H C Pandey ◽  
H Nandan
Keyword(s):  
Unit Length ◽  
Cylindrical Symmetry ◽  
Gauge Potential ◽  
Dynamical Structure ◽  
Field Equations ◽  
Abelian Gauge ◽  
Qcd Vacuum ◽  
Color Confinement ◽  
Restricted Form ◽  
Magnetic Symmetry

Using the magnetic symmetry structure of non-Abelian gauge theories of the Yang–Mills type, the mathematical foundation of dual chromodynamics in fiber-bundle form is discussed. The dual gauge potential in its restricted form is constructed in terms of magnetic vectors on global sections, which has been shown to lead the dual dynamics between topological charges and color isocharges. Constructing the Lagrangian for such dual theory, the dynamical breaking of magnetic symmetry by an effective potential is shown to push the QCD vacuum in a confining phase. The dynamical structure of the theory is investigated by deriving the field equations associated with the confining phase. The associated flux-tube structure responsible for the confinement is analyzed by computing the asymptotic string solutions of the field equations under cylindrical symmetry. Using the confining part of the dual restricted Lagrangian, the finite string energy per unit length is calculated and its implications on color confinement are discussed. PACS Nos.: 11.38Aw, 14.80Hv, 11.30Jw

Low-lying collective bands in the even tungsten isotopes 180–186W

1989 ◽  
Vol 67 (5) ◽  
pp. 479-484 ◽  
Author(s):  
R. Sahu
Keyword(s):  
Wave Function ◽  
Angular Momentum ◽  
Quadrupole Interaction ◽  
Asymmetry Parameter ◽  
Degrees Of Freedom ◽  
Energy Levels ◽  
Wave Functions ◽  
Electromagnetic Properties ◽  
Matrix Elements ◽  
Rigid Model

The γ-rigid model has been used to study the energy levels and the electromagnetic properties of 180, 182, 184, 186W. In this model, the intrinsic wave functions are obtained using the pairing plus the quadrupole–quadrupole interaction Hamiltonian of Baranger and Kumar. Good angular momentum states are projected approximately from such a triaxially symmetric intrinsic wave function. This model assumes the nucleus to be γ rigid but soft in the β degrees of freedom. The asymmetry parameter γ for a given nucleus is extracted using the experimental energies of the first 2+ and second 2+ states within the framework of the Davydov–Filippov model. The symmetry parameter β for each J state is determined from the minimization of the projected energy. The calculated energy levels of the ground and the 7 band, the B(E2) values, the electromagnetic moments, the E2 and E4 matrix elements, and the B(E2) ratios agree quite well with experimental results.

Gravity as the curvature of the wave function of the universe.

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Wave Function ◽  
Wave Functions ◽  
Main Task ◽  
Reference Systems ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Principle Of Equivalence ◽  
Relative Wave Function ◽  
New Equation ◽  
The Universe

Modern general theory of relativity considers gravity as the curvature of space-time. The theory is based on the principle of equivalence. All bodies fall with the same acceleration in the gravitational field, which is equivalent to locally accelerated reference systems. In this article, we will affirm the concept of gravity as the curvature of the relative wave function of the Universe. That is, a change in the phase of the universal wave function of the Universe near a massive body leads to a change in all other wave functions of bodies. The main task is to find the form of the relative wave function of the Universe, as well as a new equation of gravity for connecting the curvature of the wave function and the density of matter.

scholarly journals Scattering in Terms of Bohmian Conditional Wave Functions for Scenarios with Non-Commuting Energy and Momentum Operators

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 408
Author(s):  
Matteo Villani ◽  
Guillermo Albareda ◽  
Carlos Destefani ◽  
Xavier Cartoixà ◽  
Xavier Oriols
Keyword(s):  
Single Particle ◽  
Degrees Of Freedom ◽  
Single Photon ◽  
Open Quantum Systems ◽  
Wave Functions ◽  
Practical Application ◽  
Light Matter Interaction ◽  
Pure States ◽  
Energy And Momentum ◽  
Full Quantum

Without access to the full quantum state, modeling quantum transport in mesoscopic systems requires dealing with a limited number of degrees of freedom. In this work, we analyze the possibility of modeling the perturbation induced by non-simulated degrees of freedom on the simulated ones as a transition between single-particle pure states. First, we show that Bohmian conditional wave functions (BCWFs) allow for a rigorous discussion of the dynamics of electrons inside open quantum systems in terms of single-particle time-dependent pure states, either under Markovian or non-Markovian conditions. Second, we discuss the practical application of the method for modeling light–matter interaction phenomena in a resonant tunneling device, where a single photon interacts with a single electron. Third, we emphasize the importance of interpreting such a scattering mechanism as a transition between initial and final single-particle BCWF with well-defined central energies (rather than with well-defined central momenta).

scholarly journals INTEGRAL TRANSFORM TECHNIQUE FOR MESON WAVE FUNCTIONS

1996 ◽  
Vol 11 (20) ◽  
pp. 1611-1626 ◽  
Author(s):  
A.P. BAKULEV ◽  
S.V. MIKHAILOV
Keyword(s):  
Wave Function ◽  
Sum Rules ◽  
Integral Transform ◽  
Wave Functions ◽  
Sum Rule ◽  
New Approach ◽  
Exactly Solvable ◽  
The Stability ◽  
The Masses ◽  
Integral Transform Technique

In a recent paper1 we have proposed a new approach for extracting the wave function of the π-meson φπ(x) and the masses and wave functions of its first resonances from the new QCD sum rules for nondiagonal correlators obtained in Ref. 2. Here, we test our approach using an exactly solvable toy model as illustration. We demonstrate the validity of the method and suggest a pure algebraic procedure for extracting the masses and wave functions relating to the case under investigation. We also explore the stability of the procedure under perturbations of the theoretical part of the sum rule. In application to the pion case, this results not only in the mass and wave function of the first resonance (π′), but also in the estimation of π″-mass.

The Wave Theory of the Electron

1928 ◽  
Vol 24 (4) ◽  
pp. 501-505 ◽  
Author(s):  
J. M. Whittaker
Keyword(s):  
Wave Function ◽  
Differential Equations ◽  
Fourth Order ◽  
Commutative Algebra ◽  
Wave Theory ◽  
Wave Functions ◽  
Linear Differential Equations ◽  
Wave Mechanics ◽  
First Order ◽  
Linear Differential

In two recent papers Dirac has shown how the “duplexity” phenomena of the atom can be accounted for without recourse to the hypothesis of the spinning electron. The investigation is carried out by the methods of non-commutative algebra, the wave function ψ being a matrix of the fourth order. An alternative presentation of the theory, using the methods of wave mechanics, has been given by Darwin. The four-rowed matrix ψ is replaced by four wave functions ψ1, ψ2, ψ3, ψ4 satisfying four linear differential equations of the first order. These functions are related to one particular direction, and the work can only be given invariance of form at the expense of much additional complication, the four wave functions being replaced by sixteen.

LONG RANGE FORCES BETWEEN HYDROGEN MOLECULES

1955 ◽  
Vol 33 (11) ◽  
pp. 668-678 ◽  
Author(s):  
F. R. Britton ◽  
D. T. W. Bean
Keyword(s):  
Wave Function ◽  
Long Range ◽  
Ground State ◽  
Close Agreement ◽  
Van Der Waals ◽  
Wave Functions ◽  
Numerical Factor ◽  
Hydrogen Molecules ◽  
Static Quadrupole

Long range forces between two hydrogen molecules are calculated by using methods developed by Massey and Buckingham. Several terms omitted by them and a corrected numerical factor greatly change results for the van der Waals energy but do not affect their results for the static quadrupole–quadrupole energy. By using seven approximate ground state H2 wave functions information is obtained regarding the dependence of the van der Waals energy on the choice of wave function. The value of this energy averaged over all orientations of the molecular axes is found to be approximately −11.0 R−6 atomic units, a result in close agreement with semiempirical values.

scholarly journals DISTRIBUTION OF MAXIMA OF THE ANTISYMMETRIZED WAVE FUNCTION FOR THE NUCLEONS OF A CLOSED-SHELL AND FOR THE NUCLEONS OF ALL CLOSED-SHELLS IN A NUCLEUS.

2020 ◽  
Vol 15 ◽  
pp. 57
Author(s):  
G. S. Anagnostatos
Keyword(s):  
Wave Function ◽  
Mathematical Problem ◽  
Closed Shell ◽  
Wave Functions ◽  
Pictorial Representation ◽  
One Dimensional ◽  
Regular Polyhedra ◽  
Closed Shell Nuclei ◽  
Simple Systems ◽  
Closed Shells

The significant features of exchange symmetry are displayed by simple systems such as two identical, spinless fermions in a one-dimensional well with infinite walls. The conclusion is that the maxima of probability of the antisymmetrized wave function of these two fermions lie at the same positions as if a repulsive force (of unknown nature) was applied between these two fermions. This conclusion is combined with the solution of a mathematical problem dealing with the equilibrium of identical repulsive particles (of one or two kinds) on one or more spheres like neutrons and protons on nuclear shells. Such particles are at equilibrium only for specific numbers of particles and, in addition, if these particles lie on the vertices of regular polyhedra or their derivative polyhedra. Finally, this result leads to a pictorial representation of the structure of all closed shell nuclei. This representation could be used as a laboratory for determining nuclear properties and corresponding wave functions.

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