arXiv subjects

Ying-Qiu Gu

Publications and source records attributed to Ying-Qiu Gu.

At least 19 recordsLinked to original sources

arXiv2018

Mass Spectrum of Dirac Equation with Local Parabolic Potential

In this paper, we solve the eigen solutions and mass strectra of the Dirac equation with local parabolic potential which is approximately equal to the short distance potential generated by spinor itself. The mass spectrum is quite different from that of a spinor in Coulomb potential. The masses of some baryons are similar to this one. The mass-angular momentum relation $m=m(J,n)$ is quite similar to the Regge trajectories. The parabolic potential has property of asymptotic freedom near the center and confinement at large distance. So the results imply that, the local parabolic potential may be more suitable for describing nuclear potential approximately. The solving procedure can also be used to solve the Dirac equation with other complicated potential.

hep-th↗

arXiv2017

Local Lorentz Transformation and Mass-Energy Relation of Spinor

In this paper, we strictly establish classical concepts and relations according to a Dirac equation with scalar, vector and nonlinear potentials. To calculate classical parameters for moving spinor, the local Lorentz transformations for parameters are derived. The calculation shows that different kinds of potentials result in different energy-speed relations, and the energy-speed relations for these potentials are derived in detail. The usual mass-energy relation $E = mc^2$ holds only for the linear spinor. The energy-speed relations can be used as fingerprints to identify the interactive potentials of a particle by elaborated experiments. The analysis and results of this paper can also provide some natural explanations for the foundation of quantum mechanics, and clarify some long-standing puzzles in the theory.

hep-th↗

arXiv2017

Light-Cone Coordinate System in General Relativity

If there is a null gradient field in 1+3 dimensional space-time, we can set up a kind of light-cone coordinate system in the space-time. In such coordinate system, the metric takes a simple form, which is much helpful for simplifying and solving the Einstein's field equation. This light-cone coordinate system has wonderful properties and has been widely used in astrophysics to calculate parameters. In this paper, we give a detailed discussion for the structure of space-time with light-cone coordinate system. We derive the conditions for existence of such coordinate system, and show how to construct the light-cone coordinate system from usual ones, then explain their geometrical and physical meanings by examples.

physics.gen-ph↗

arXiv2017

The Vierbein Formalism and Energy-Momentum Tensor of Spinors

To study the coupling system of space-time and Fermions, we need the explicit form of the energy-momentum tensor of spinors. The energy-momentum tensor is closely related to the tetrad frames which cannot be uniquely determined by the metric. This flexibility increases difficulties to derive the exact expression and easily leads to ambiguous results. In this paper, we give a detailed derivation for the energy-momentum tensor of Weyl and Dirac spinors. From the results we find that, besides the usual kinetic energy momentum term, there are three kinds of other additional terms. One is the nonlinear self-interactive potential, which acts like negative pressure. The other reflects the interaction of momentum $p^μ$ with tetrad. The third is the spin-gravity coupling term which is a higher order infinitesimal in weak field, but may be important in a neutron star. This term is also closely related with magnetic field of a celestial body. These results are based on the decomposition of usual spin connection into geometrical part and dynamical part, which not only makes calculation simpler, but also highlights their different physical meanings. In addition, we get a new tensor $S^{μν}_{ab}$ in calculation of tetrad formalism, which plays an important role in the interaction of spinor with gravity.

gr-qc↗

arXiv2017

A Procedure to Solve the Eigen Solution to Dirac Equation

In this paper, we provide a procedure to solve the eigen solutions of Dirac equation with complicated potential approximately. At first, we solve the eigen solutions of a linear Dirac equation with complete eigen system, which approximately equals to the original equation. Take the eigen functions as base of Hilbert space, and expand the spinor on the bases, we convert the original problem into solution of extremum of an algebraic function on the unit sphere of the coefficients. Then the problem can be easily solved. This is a standard finite element method with strict theory for convergence and effectiveness.

physics.gen-ph↗

arXiv2017

The Simplification of Spinor Connection and Classical Approximation

The standard spinor connection in curved space-time is represented in a compact form. In this form the calculation is complicated, and its physical effects are concealed. In this paper, we split spinor connection into two vectors $Υ_μ$ and $Ω_μ$, where $Υ_μ$ is only related to geometrical calculations, but $Ω_μ$ leads to dynamical effects, which couples with the spin of a spinor. The representation depends only on metric but is independent of Dirac matrices, so it is valid for both Weyl spinors and Dirac spinor. In the new form, we can clearly define classical concepts for a spinor and then derive its complete classical dynamics. By detailed calculation we find the classical approximation is just Newtonian second law. The dynamical connection $Ω_μ$ couples with the spin of a particle with a tiny energy in weak field, which provides location and navigation functions for a spinor. This term may be also important to form magnetic field of a celestial star. From the results, we find the spinor has marvelous structure and wonderful property, and the interaction between spinor and gravity is subtle. This study may be also helpful to clarify the relations between relativity, quantum mechanics and classical mechanics.

gr-qc↗

arXiv2017

Natural Coordinate System in Curved Space-time

In this paper we establish a generally and globally valid coordinate system in curved space-time with the simultaneous hypersurface orthogonal to the time coordinate. The time coordinate can be preseted according to practical evolving process and keep synchronous with the evolution of the realistic world. In this coordinate system, it is convenient to express the physical laws and to calculate physical variables with clear geometrical meaning. We call it "natural coordinate system". The constructing method for the natural coordinate system is concretely provided, and its physical and geometrical meanings are discussed in detail. In NCS we make classical approximation of spinor equation to get Newtonian mechanics, and then make weak field approximation of Einstein's equation and low speed approximation of particles moving in the space-time. From the analysis and examples we find it is a nice coordinate system to describe the realistic curved space-time, and is helpful to understand the nature of space-time.

gr-qc↗

arXiv2017

Functions of State for Spinor Gas in General Relativity

The energy momentum tensor of perfect fluid is a simplified but successful model in astrophysics. In this paper, assuming the particles driven by gravity and moving along geodesics, we derived the functions of state in detail. The results show that, these functions have a little correction for the usual thermodynamics. The new functions naturally satisfy the causal condition and consist with relativity. For the self potentials of the particles we introduce an extra function $W$, which acts like negative pressure and can be used to describe dark matter. The results are helpful to understand the relation and interaction between space-time and matter.

physics.gen-ph↗

arXiv2017

Nonlinear Spinors as the Candidate of Dark Matter

In this paper, we discuss the equation of state for nonlinear spinor gases in the context of cosmology. The mean energy momentum tensor is similar to that of the prefect fluid, but an additional function of state $W$ is introduced to describe the nonlinear potential. The equation of state $w(a)\lesssim -1$ in the early universe is calculated, which provides a natural explanation for the negative pressure of dark matter and dark energy. $W$ may be also the main origin of the cosmological constant $Λ$. So the nonlinear spinor gases may be a candidate for dark matter and dark energy.

physics.gen-ph↗

arXiv2017

Dynamical Constraints on the Cosmological Parameters

In cosmology, the cosmic curvature $K$ and the cosmological constant $Λ$ are two important parameters, and the values have strong influence on the behavior of the universe. In the context of normal cosmology, under the ordinary assumptions of positive mass-energy and initial negative pressure, we find the initial singularity of the universe is certainly absent and we have $K=1$. This means total spatial structure of the universe should be a 3-dimensional sphere $S^3$. For the cyclic cosmological model, we have $Λ\lesssim 10^{-24} {\rm ly}^{-2}$. Obviously, such constraints would be helpful for the researches on the properties of dark matter and dark energy in cosmology.

gr-qc↗

arXiv2017

Some Subtle Concepts in Fundamental Physics

In this paper, we discuss some subtle concepts, such as coordinate, measurement, simultaneity, Lorentz-FitzGerald contraction, singularity in fundamental physics. The explanations of these concepts in textbooks are usually incomplete and lead to puzzles. Some long-standing paradoxes such as the Ehrenfest one are caused by misinterpretation of these concepts. The analysis shows these concepts all have simple and naive meanings, and can be well understood using suitable logical procedure. The discussion may shed light on some famous paradoxes, and provide some new insights into the structure and features of a promising unified field theory.

physics.gen-ph↗

arXiv2017

Test of Einstein's Mass-Energy Relation

The Einstein's mass-energy relation $E=mc^2$ is one of the most fundamental formulae in physics, but it has not been seriously tested by an elaborated experiment, and only some indirect evidences in nuclear reaction suggested that it holds to high precision. Manifestly, for a particle, different self potential leads to different energy-speed relation, which can be used as the fingerprints of them. In this letter, we propose an experiment to test this relation. The experiment only involves low energy of particles and measurement of speed, which can be easily realized. The experiment may shed lights on a number of fundamental puzzles in physics.

hep-th↗

arXiv2017

Integrable conditions for Dirac Equation and Schrödinger equation

By constructing the commutative operators chain, we derive the integrable conditions for solving the eigenfunctions of Dirac equation and Schrödinger equation. These commutative relations correspond to the intrinsic symmetry of the physical system, which are equivalent to the original partial differential equation can be solved by separation of variables. Detailed calculation shows that, only a few cases can be completely solved by separation of variables. In general cases, we have to solve the Dirac equation and Schrödinger equation by effective perturbation or approximation methods, especially in the cases including nonlinear potential or self interactive potentials.

physics.gen-ph↗

arXiv2017

Functions and Relations for an Evolving Star with Spherical Symmetry

In this paper, we drive and simplify some important equations and relations for an evolving star with spherical symmetry, and then give some simple analysis for their properties and implications. In the light-cone coordinate system, these equations and relations have a normal and neat form which is much accessible than the usual Einstein field equation. So they may be helpful for students to study general relativity and for researchers to do further discussion.

physics.gen-ph↗

arXiv2009

Some Paradoxes in Special Relativity

The special theory of relativity is the foundation of modern physics, but its unusual postulate of invariant vacuum speed of light results in a number of plausible paradoxes. This situation leads to radical criticisms and suspicions against the theory of relativity. In this paper, from the perspective that the relativity is nothing but a geometry, we give a uniform resolution to some famous and typical paradoxes such as the ladder paradox, the Ehrenfest's rotational disc paradox. The discussion shows that all the paradoxes are caused by misinterpretation of concepts. We misused the global simultaneity and the principle of relativity. As a geometry of Minkowski space-time, special relativity can never result in a logical contradiction.

physics.gen-ph↗

arXiv2009

The Characteristic Functions and Their Typical Values for the Nonlinear Spinors

In this paper, we solve the eigen solutions to some nonlinear spinor equations, and compute several functions reflecting their characteristics. The numerical results show that, the nonlinear spinor equation has only finite meaningful eigen solutions, which have positive discrete mass spectra and anomalous magnetic moment. The nonlinear potential and interactions yield different contributions to the total energy, and these components of the energy lead to different energy-speed relation. The magnitude of these components can be detected by elaborate experiments. The weird properties of the nonlinear spinors might be closely related with the elementary particles and their interactions, so some deeper investigations on them are significant.

hep-th↗

arXiv2009

Stationary Spiral Structure and Collective Motion of the Stars in a Spiral Galaxy

Most fully developed galaxies have a vivid spiral structure, but the formation and evolution of the spiral structure are still an enigma in astrophysics. In this paper, according to the standard Newtonian gravitational theory and some observational facts, we derive an idealized model for spiral galaxy, and give a natural explanation to the spiral structure. We solve some analytic solutions to a spiral galaxy, and obtain manifest relations between density and speed. From the solution we get some interesting results: (I) The spiral pattern is a stationary or static structure of density wave, and the barred galaxy globally rotate around an axis at tiny angular speed. (II) All stars in the disc of a barred spiral galaxy move in almost circular orbits. (III) In the spiral arms, the speed of stars takes minimum and the stellar density takes maximum. (IV) The mass-energy density of the dark halo is compensatory for that of the disc, namely, it takes minimum in the spiral arms. This phenomenon might reflect the complicated stream lines of the dark halo.

physics.gen-ph↗

arXiv2009

The Exact Solutions to the Gravitational Contraction in Comoving Coordinate System

The gravitational collapse of a star is a warmly discussed but still puzzling problem, which not only involves the dynamics of the gases, but also the subtle coordinate transformation. In this letter, we give some more detailed investigation on this problem, and reach the results: (I). The comoving coordinate system for the stellar system is only compatible with the zero-pressure free falling particles. (II). For the free falling dust, there are three kind of solutions respectively corresponding to the oscillating, the critical and the open trajectories. The solution of Oppenheimer and Snyder is the critical case. (III). All solutions are exactly derived. There is a new kind singularity in the solution, but its origin is unclear.

gr-qc↗