Ying-Qiu Gu

• PhD
• Engineer at Fudan University

The nonlinear Dirac equation is a magical equation that hides many mysteries of nature, so it is worth systematic study. In this paper, we give a detailed analysis for the effects of various covariant potential terms on the energy eigenstates and the representation space as well as the solvability of the spinor equation, and we obtain the specific...

This paper presents several unresolved problems that the author has encountered in the study of unified field theory and seeks input from colleagues in the field. These problems include the algebraic and variational relations between frames and the metric, the negative energy confinement of the nonlinear spinor field and its relationship with the P...

"J. Geom. Symmetry Phys. 66: 1-34 (2023). DOI: 10.7546/jgsp-66-2023-1-34"-----Relativity and quantum theory are two epoch-making theories of 20th century physics, which not only established modern material civilization, but also changed people's world view. However, the Copenhagen interpretation of quantum mechanics remains a controversial issue. T...

The goal of this book is to study the unified field theory; that is, to logically derive all physical laws from a few simple principles. This goal is also the common dream of great thinkers who all agree that nature is governed by several extremely simple mathematical rules, and pure thought can grasp reality. Einstein spent most of his life in pur...

The interaction between spinors and gravity is the most complicated and subtle interaction in the universe, which involves the basic problem to unified quantum theory and general relativity. By means of Clifford Algebra, a unified language and tool to describe the rules of nature, this paper systematically discusses the dynamics and properties of s...

“All is Number"-----the universe follows a few profound mathematical rules, and pure thought can grasp reality. This paper explores the first principles of fundamental physics, focusing on the principle of relativity, the principle of least action, and the principle of regularity. By reviewing the development of the principle of relativity and illu...

Gu, Y.Q. (2025) First Principles in Fundamental Physics. J. Appl. Math. Phys., 13, 1473-1499. https://doi.org/10.4236/jamp.2025.134079 “All is number”—the universe follows a few profound mathematical rules, and pure thought can grasp reality. This paper explores the first principles of fundamental physics, focusing on the principle of relativity,...

“All is Number"-----the universe follows a few profound mathematical rules, and pure thought can grasp reality. This paper explores the first principles of fundamental physics, focusing on the principle of relativity, the principle of least action, and the principle of regularity. By reviewing the development of the principle of relativity and illu...

"Gu, Y.-Q. (2024) Some Mathematical Problems in Fundamental Physics. J. Geom. Symmetry Phys., 70, 1-36." A good problem is the starting point of expanding the territory of science. This paper presents several unresolved problems that the author has encountered in the study of unified field theory and seeks input from colleagues in the field. These...

"Gu, Y.-Q. (2024) Some Mathematical Problems in Fundamental Physics. J. Geom. Symmetry Phys., 70, 1-36." 好的问题是扩展科学疆域的起点和阶梯。本文汇编了作者在研究统一场论过程中遇到了但没有解决好的几个问题，整理出来向诸位同仁请教. 这些问题包括标架与度规的代数与变分关系，超复数的零模集的意义，非线性旋量场的负能禁闭以及与Pauli不相容原理的关系，奇点定理的反例与动力学分析等，都具有明确的物理意义。本文简略地介绍了问题的背景材料和已有的一些进展，以便于读者快速理解问题的本质和现状。这些问题的解决，可能会提升人们对大自然深层规律的认识。 Keywords: Hypercomplex num...

In this paper we discuss the dynamic effects of the varying frames. The differential of frame or basis vectors is always equivalent to a linear transformation of the frame, and the linear transformation is not the same in different contexts. In differential geometry, the linear transformation is the connection operator. While in quantum mechanics,...

"Gu, Y. and Ning, G. (2024) Ozone Sterilizer for Treatment and Health Care. Journal of Biosciences and Medicines, 12, 156-163. doi: 10.4236/jbm.2024.122012." Ozone is a green broad-spectrum bactericidal disinfectant, and a trace amount of ozone in the atmosphere makes many viruses and bacteria lose their biochemical activity and infectivity. Nature...

The phenomenon of ``missing mass'' in galaxies has triggered new theoretical exploration, forming a competition between dark matter assumption, modified Newtonian dynamics and modified gravity. Over the past forty years, various versions of the modified scenario have been proposed to simulate the effects of missing mass. These schemes replace the d...

星系中“失踪质量”现象引发了新的理论探讨，形成了暗物质假设、修改牛顿力学与修改引力理论的方案之间的竞争局面。在过去的四十多年里，各种版本的修正方案被提出来模拟“失踪质量”的影响。这些方案通过在动力学方程中引进一些数值很小的额外力项，以取代暗物质的作用。额外力项主要在星系大尺度上发挥作用，例如拟合Tully-Fisher关系或者渐近平坦的旋转曲线。本文的讨论表明，把修正方案作为基础理论的证据目前还是很不充分的。本文用爱因斯坦场方程的弱场和低速近似得到简化的星系动力学方程组，再用这个方程组讨论了星系动力学中的两个重要的经验关系，即Faber-Jackson关系和Tully-Fisher关系，以及相关的基本面问题。这些讨论为改进经验关系的弥散程度提供了参考方案，也为广义相对论在分析暗物质性质和求解...

"Journal of Geometry and Symmetry in Physics 67:65-85, 2024. DOI: 10.7546/jgsp-67-2024-65-85" The nonlinear Dirac equation is a magical equation that hides many mysteries of nature, so it is worth systematic study. In this paper, we give a detailed analysis for the effects of various covariant potential terms on the energy eigenstates and the repre...

People's Daily life and physical health are often plagued by viruses and bacteria. The novel coronavirus epidemic several years ago has seriously affected the global economy and social life. In addition to vaccination, ecologically safe and long-term and effective disinfection methods are very necessary. Ozone is an effi cient and broad-spectrum ba...

“Gu Y. Differentials of the basis in Clifford Geometric Algebra. Journal of AppliedMath. 2024; 2(4): 1700. https://doi.org/10.59400/jam.v2i4.1700” In this paper we discuss the dynamic effects of the varying frames. The differential of frame or basis vectors is always equivalent to a linear transformation of the frame, and the linear transformatio...

Clifford 代数基元素的一组标准正交矩阵表示，建立了 Clifford 代数与微分 几何的联系， 通过定义基矢量的联络算子， 把原来复杂易错的微分几何概念简化为代数关系， 从而大大简化了微分几何的很多内容。进一步的分析表明，物理量及其运算具有 Clifford 代 数结构和超复数形式，可简化为矩阵代数的加减乘除算术运算。因此，整个理论物理学在 Clifford 代数和变分原理的基础上统一起来了，简洁规范，优雅美观，原来很难处理的问题 变得直观易懂。这将大大提高学习基础知识的效率，也为深入研究提供了深邃的洞察力。 成果 2：相对论中的概念问题与合理解释-自然坐标系 代表作品： [5] Gu Y Q. Natural Coordinate System in Curved Space-Ti...

“Gu YQ. Miraculous hypercomplex numbers. Mathematics and Systems Science 2023; 1(1): 2258.”-----The development of number system has gone through a long and difficult process, and many landmark concepts and theorems were put forward. By briefly reviewing the development of hypercomplex systems, the constructing rules of the unit elements are discus...

"In ATINER's Conference Paper Proceedings Series, PHY2023-0290 . Athens, Greece: ATINER. 2023. ISSN:2529-167X. "---The origin and evolution of the celestial magnetic field remains an unsolved mystery. Many hypotheses have been proposed to explain the origin, but each hypothesis has some insurmountable difficulties. Currently, the widely accepted th...

本书研究统一场论，从很少几条简单明了的基本原理出发，逻辑地推导所有的物理定律。大自然由几个极其简单的数学规则所控制，纯粹思维可以把握实在。本文采用克利福德代数和变分原理作为基本的数学工具，后来又推广为超复数。超复数为众多复杂的数学和物理理论提供了统一、标准、优雅和开放的语言和工具，具有加减乘除运算，每个人都能很好地理解。超复数是科学和工程技术的统一语言和工具，有望为整个科学知识体系提供新的大综合。 经过协商，出版社同意公开发布本书的电子版。原书中存在少量的打印或翻译错误，例如P234页（10.1.60）式后的用泡利矩阵表示四元数基应为-iσk, P237页（10.1.87）后的 “线性连续函数” 应为“线性连续泛函”等，希望读者注意并及时反馈有关错误。 This book studies...

"J. Geom. Symmetry Phys. 66: 1-34 (2023). DOI: 10.7546/jgsp-66-2023-1-34"----相对论和量子论是20世纪物理学的两个划时代理论，它们不但创造了现代物质文明，而且改变了人们的世界观。但是，量子力学的哥本哈根诠释仍是一个备受争议的问题。哥本哈根诠释认为微观粒子的运动具有不确定性，波函数的模平方是发现粒子的概率密度。但实际上，波函数是比概率密度内涵丰富得多的概念。一个旋量场完整地描述了一个基本粒子的全部性质，可以定义一个粒子的所有力学量，而且旋量场方程在逻辑上包含了经典力学和量子力学。抽象算子代数在量子力学中的广泛应用，进一步增加了量子理论的神秘感和迷惑性，但是算子代数对微观粒子的描述是不全面的。本文以旋量场方程为逻辑前提来...

Hypercomplex number systems are vector algebras with the definition of multiplication and division of vectors, satisfying the associativity and distributive law. In this paper, some new types of hypercomplex numbers and their fundamental properties are introduced, the Clifford algebra formalisms of hydrodynamics and gauge field equations are establ...

Relativity and quantum theory are two epoch-making theories of 20th century physics, which not only established modern material civilization, but also changed people’s world view. However, the Copenhagen interpretation of quantum mechanics remains a controversial issue. The Copenhagen interpretation holds that the motion of the microscopic particle...

"Gu, Y. Q. (2024). Pauli Exclusion Principle and Nonlinear Dirac Equation. J. Geom. Symmetry Phys. 67, 65-85." The nonlinear Dirac equation is a magical equation that hides many mysteries of nature, so it is worth systematic study. In this paper, we give a detailed analysis for the effects of various covariant potential terms on the energy eigenst...

"Journal of Geometry and Symmetry in Physics 67:65-85, 2024. DOI: 10.7546/jgsp-67-2024-65-85". 非线性狄拉克方程是隐藏了很多大自然奥秘的神奇方程，因此值得系统研究。本文详细分析了狄拉克方程中各种协变势能项对能量本征态的影响，以及解的表示空间和可解性，得到了存在驻波解的势能项的具体形式。通过简化旋量方程我们发现，赝标势引起本征解的径向分量震荡不收敛，因此旋量之间的非线性弱相互作用可能是泡利不相容原理的动力学原因。旋量的非线性项具有一些奇妙的性质，例如负能态禁闭，产生负压力和天体磁场等，因此值得深入研究。本文还给出了求解具有复杂势能项的狄拉克方程的计算方法，对进一步揭开基本粒子的神秘面纱可能是一套有效的...

If general relativity is correct, then the origin of the universe is a simple mathematical problem. The Friedmann equation in cosmology is a well-structured ordinary differential equation, and the global properties of its solutions can be qualitatively analyzed by the phase-trajectory method. In this paper we show that the total energy density of m...

“Gu Y-Q. Why the big bang never happened. Mathematics and Systems Science. 2024; 2(2): 2630. DOI: 10.54517/mss.v2i2.2630” 如果广义相对论的基本框架没有问题，那么宇宙的起源就只是一个简单的数学问题。宇宙学中弗里德曼方程是一个具有良好结构的常微分方程，可以用相轨道方法定性分析解的整体性质。本文研究表明，宇宙中所有物质的总能量密度是正的，奇点附近的总压力是负的。根据这两个物态条件分析弗里德曼方程解的整体性质，我们发现宇宙大爆炸不可能发生，宇宙空间必是封闭的三维球面，宇宙学常数很可能是零，宇宙演化在时间上应该是循环的。由于分析和论证都简单明了，因此这些结论应该是可靠的。 关键词...

"Advances in International Applied Mathematics. 2023; 5: (3) ; 9-18 " 相对论存在一些概念上的误区，因此产生了不少似是而非的佯谬，争论了一个多世纪。 本文通过实例严格分析了相对论中坐标系和同时性等基本概念，揭示了现实时空只存在一个 整体同时超曲面，现实世界的演化具有同步性，同时性具有客观性和唯一性。整体同时超 曲面定义了客观宇宙时间以及与这个宇宙时间垂直的客观空间，进而建立了一个普遍有效的 "自然坐标系"。自然坐标系具有特殊的物理意义，其空间坐标相对 于宇宙微波背景是静止的，g tt 描述了引力场，不能并入时间坐标。通常的观点把时间坐标的 等时性等同于世界演化的同步性，混淆了客观的现实时空和人为设定的坐标系，因此产生了 逻辑...

本文介绍了几种改善变压吸附制氧机效率、氧浓度和稳定性方面的技术措施。通过增设一个辅助罐体，储存制氧末期80%左右的富氧气体作为清洗用气，可以提高产品氧气产量的同时，得到浓度稳定在93%以上的产品氧气。通过增加氧气纯化器可以得到浓度99%的高浓度氧气。通过吸附塔的双层封头防粉化结构，可以有效防止分子筛的粉化现象，并能方便现场更换分子筛。这些措施简单实用，值得推广。 关键词 变压吸附；空分制氧；纯化过程；分子筛粉化 Several technical methods to improve the efficiency, oxygen concentration and stability of the pressure swing adsorption oxygen generator are...

“Gu YQ. Miraculous hypercomplex numbers. Mathematics and Systems Science 2023; 1(1): 2258.”-----数系的发展经历了一个漫长而艰难的历程，许多里程碑意义的概念和定理被建立起来。本文通过简要回顾了超复数系的发展过程，分析了超复数基的构成规则。超复数作为定义了向量乘法、除法和范数的向量空间，综合了代数、几何和分析等数学工具的优点，忠实地描述了时空和物理系统的内在性质，为基础科学和工程技术提供了统一的语言和有力的工具。在超复数的应用中，标准基的结合性和可逆性等类群性质才是最重要的，零因子对代数运算并没有大的影响。基元素的乘法表完全描述了超复数的内在性质，由乘法表构造的矩阵$\A$满足结构方程$\A^2=n...

"Geometry, Integrability and Quantization 25:47-72, 2023"------ Number systems are number sets closed for addition, subtraction, multiplication and division operations. If the zero-factor condition is relaxed, then we can define a large number of new number systems of good properties and high application value. In this paper, we first introduce so...

"Geometry, Integrability and Quantization 25:47-72, 2023"------ 数系是关于加减乘除运算封闭的集合，如果放宽零因子条件，我们可以定义大量性质优良且应用价值较高的新数系。本文首先介绍了一些新型的超复数系和基本性质。然后建立了流体动力学方程和规范场方程的克利福德代数形式，并导出了一些新颖的相容性条件。这些条件可能有助于理解非线性物理方程解的性质。本文还简单讨论了超复数系的坐标变换和协变导数的问题。超复数是实数、复数、四元数和向量代数的统一和推广。它结合了代数、几何和数学分析等重要功能，准确、完整地描述了时空和物质的内在特性，为基础科学理论和工程技术提供了统一、标准、优雅的语言和工具。 用超复数描述数学、物理和工程问题具有形式简洁、结...

"2022Journal of Geometry and Symmetry in Physics 64:9-22"-----By means of hypercomplex numbers, in this paper we discuss algebraic equations and obtain some interesting relations. A structure equation A2=nA of a group is derived. The matrix representation of a group constitutes the basis elements of a hypercomplex number system. By a canonical real...

The COVID-19 has tyrannized the world for almost 3 years and has seen no signs of decline. The mutant Omicron is more infectious and can be transmitted and spread through many channels. As long as there is any residue, the virus can quickly revive and spread if there is no intervention. In addition to targeted prevention and control and vaccination...

Clifford algebra is a unified language and efficient tool for geometry and physics. In this paper, we derive the integrable conditions for Dirac and Pauli equations by Clifford algebra, which shows Clifford algebra has a standard operation procedure and deep insights into the structure of the equations. Here the integrable conditions are only regar...

These researches take Clifford algebra and variational principles as basic mathematical tools, with a unified view and axiomatic method, to derive most of the mature laws of physics, logically reconstruct the building of theoretical physics, and also get some new conclusions different from the traditional results. The researches organize almost all...

Integrated solar heating and plateau ecological dwellings “中国科技人才，2022; 89(6):11-13.” Abstract: This paper introduces a passive solar heating scheme integrated with the buildings. This technical scheme directly uses hollow tempered glass as the sunny roof of the house, and the sunlight directly shines on the heat storage plates as the furred ceil...

The Clifford algebra is a unification and generalization of real number, complex number, quaternion, and vector algebra, which accurately and faithfully characterizes the intrinsic properties of space-time, providing a unified, standard, elegant, and open language and tools for numerous complicated mathematical and physical theories. So it is worth...

Galactic dynamics is the foundation for simulating galactic structure and for solving other problems. However, the traditional dynamic equations include some unreasonable assumptions and are therefore scientifically invalid. In this paper, by introducing the following three working assumptions, we established the galactic dynamics of high precision...

The description of the microscopic world in quantum mechanics is very different from that in classical physics, and there are some points of view that are contrary to intuition and logic. The first is the problem of reality; quantum mechanics believes the behavior of micro particles is random and jumping. The second is the loss of certainty; the co...

By means of hypercomplex numbers, in this paper we discuss algebraic equations and obtain some interesting relations. A structure equation $A^2=nA$ of a group is derived. The matrix representation of a group constitutes the basis elements of a hypercomplex number system. By a canonical real matrix representation of a cyclic group, we define the cyc...

“辜英求, 高等数学研究. 2024,27(1) :37-46” 本文是一篇介绍Clifford代数基本性质和应用的文章。Clifford代数是实数、复数、四元数和向量代数的统一和推广，它准确、忠实地刻画了时空的内在性质，为众多数学和物理理论提供了统一、标准、优雅和开放的语言和工具，值得在本科物理和数学的教学中普及。回顾数系理论的发展和完善的漫长历史，我们发现包括克利福德代数在内的超复数系，在自然科学中占据核心位置。超复数的零模集是具有特殊几何意义的低维集合，就像现实时空中的光锥，对代数运算没有实质性影响。克利福德代数以统一的方式描述复数和四元数，并且可以直接地推广到2n元结合代数。在这个推广中，时空中标准正交基的矩阵表示起了重要作用。矩阵表示具有抽象概念难以表达的内容，例如行列式和逆元的定...

By analyzing the energy-momentum tensor and equations of state of ideal gas, scalar, spinor and vector potential in detail, we find that the total mass density of all matter is always positive, and the initial total pressure is negative. Under these conditions, by qualitatively analyzing the global behavior of the dynamical equation of cosmological...

By means of Clifford Algebra, a unified language and tool to describe the rules of nature, this paper systematically discusses the dynamics and properties of spinor fields in curved space-time, such as the decomposition of the spinor connection, the classical approximation of the Dirac equation, the energy-momentum tensor of spinors and so on. To s...

The magnetic field of the earth plays an important role in the ecosystem, and the magnetic field of celestial bodies is also important in the formation of cosmic large-scale structures, but the origin and evolution of the celestial magnetic field is still an unresolved mystery. Many hypotheses to explain the origin have been proposed, but there are...

My postdoctoral report “The Discussion of Some Fundamental Problems in Physics”.

By analyzing the energy-momentum tensor and equations of state of ideal gas, scalar, spinor and vector potential in detail, we find that the total mass density of all matter is always positive, and the initial total pressure is negative. Under these conditions, by qualitatively analyzing the global behavior of the dynamical equation of cosmological...

In this note we construct explicit complex and real faithful matrix representations of the Clifford algebras $\Cl_{p,q}$. The representation is based on Pauli matrices and has an elegant structure similar to the fractal geometry. In the cases $p+q=4m$, the representation is unique in equivalent sense, and the $1+3$ dimensional space-time correspond...

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 var...

In this chapter, we provide some enlightening examples of the application of Clifford algebra in geometry, which show the concise representation, simple calculation, and profound insight of this algebra. The definition of Clifford algebra implies geometric concepts such as vector, length, angle, area, and volume and unifies the calculus of scalar,...

In this paper, we derive and simplify some important equations and relations for a relativistic 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 more accessible than the usual E...

Clifford algebra is a unified language and efficient tool for geometry and physics. In this paper, we derive the integrable conditions for Dirac and Pauli equations by Clifford algebra, which shows Clifford algebra has a standard operation procedure and deep insights into the structure of the equations. Here the integrable conditions are only regar...

Most fully developed galaxies have vivid spiral structure, but the formation and evolution of spiral structure is still a mystery that is not fully understood in astrophysics. We find that the currently used equations of galactic dynamics contain some unreasonable components. In this paper, the following three working assumptions are introduced to...

The description of the microscopic world in quantum mechanics is very different from that in classical physics, and there are some points of view that are contrary to intuition and logic. The first is the loss of reality, the behavior of micro particles shows randomness and hopping. The second is the loss of certainty, the conjugate physical variab...

In this paper, we introduce a series stable algorithms for solving the stiff ordinary differential equation system(ODE). These algorithms are based on the solution to the locally linearized perturbation equation and its corresponding Pade approxima- tions. The algorithms get ride of the influence of the stiffness and have explicit schemes. In contr...

In this paper, we provide some enlightening examples of the application of Clifford algebra in geometry, which show the concise representation, simple calculation and profound insight of this algebra. The definition of Clifford algebra implies geometric concepts such as vector, length, angle, area and volume, and unifies the calculus of scalar, spi...

The description of the microscopic world in quantum mechanics is very different from that in classical physics, and there are some points of view that are contrary to intuition and logic. The first is the loss of reality, the behavior of micro particles shows randomness and hopping. The second is the loss of certainty, the conjugate physical quanti...

Clifford algebra is a natural language to express theories of fields and space-time. In this wonderful language, we derive the integrable conditions for solving the eigen-functions of Dirac equation. We find the commutators expressed by Clifford numbers have a simple, unified and covariant form, which are different from the usual representation. Ph...

In this paper, we provide some enlightening applications of Clifford algebra in physics. Directly taking the generators of Clifford algebra as tetrad of space-time, we redefine some concepts of field and then discuss the dynamical equation and symmetry by Clifford calculus. Clifford algebra exactly reflects intrinsic symmetry of fields with no more...

According to a framework based on Clifford algebra Cℓ(1,3), this paper gives a classification for elementary fields, and then derives their dynamical equations and transformation laws in detail. These results provide an outline on elementary fields and some new insights into their unusual properties. All elementary fields exist in pairs, and one pa...

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...

"Gu Y-Q. A Note on the Representation of Clifford Algebras. J. Geom. Symmetry Phys. 2021; 62: 29-52.doi:10.7546/jgsp-62-2021-29-52" In this note we construct explicit complex and real faithful matrix representations of the Clifford algebra $Cl_{p,q}$. The representation is based on Pauli matrices and has an elegant structure similar to the fractal...

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 relati...

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 w...

In this letter 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 convenien...

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 weird properties of th...

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...

In this paper, we solve the eigen solutions to the Dirac equation with local par-abolic potential approximately. The energy spectrum is quite different from that with Coulomb potential. The mass spectrum of some baryons is similar to this one. The results also show that, the local parabolic potential may be more suitable for describing the nuclear...

In fundamental theories of physics, the dynamical equations all have time inversion invariance. Except for the evolution of some simple system which has realistic inverse processes, but for a slightly more complicated system, the evolution processes are irreversible. This is the problem of arrow of time, which is always warmly debated. In different...

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,...

Gu Y-Q. Some Paradoxes in Special Relativity and the Resolutions “Advances in Applied Clifford Algebras 21(1):103-119, 2011. arXiv:0902.2032” 狭义相对论是现代物理的基础，但其不同寻常的真空光速不变性原理导致 很多似是而非的悖论或佯谬。这种状况使得很多人对相对论的真理性提出尖锐的质疑和批评。在数学上看，相对论是关于时空的几何学。从这种观点出发，我们可以 得到关于一些典型佯谬如梯子佯谬、转碟佯谬等的统一解释。从解释中可以看出， 这些佯谬都是由于曲解概念引起的，是误用整体同时性和相对性原理造成的。作为 闵科夫斯基时空的几何学，相对论是不会导致逻辑矛盾的。...

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...

“Gu, Ying-Qiu, Physics Essays, Volume 30, Number 4, December 2017, pp. 356-363(8)” 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-st...

The multipole moments method is not only an aid to understand the deformation of the space-time, but also an effective tool to solve the approximate solutions of the Einstein field equation. However, The usual multipole moments are recursively defined by a sequence of symmetric and trace-free tensors, which are inconvenient for practical resolution...

In order to explain the present accelerating expansion of the universe and the related dark energy with negative pressure, the scalar model and cosmological factor have been widely studied. Relatively, the spinor field is unreasonably overlooked. Considering the facts that all fermions are described by spinors and the uniform scalar field can hardl...

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 s...

By constructing the commutative operators chain, we derive the integrable conditions for solving the eigenfunctions of Dirac equation and Schr\"odinger 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 v...

In this paper, we provide a simplified stellar structure model for ideal gases, in which the particles are only driven by gravity. According to the model, the structural information of the star can be roughly solved by the total mass and radius of a star. To get more accurate results, the model should be modified by introducing other interaction am...

In this paper, we examine the dynamical behavior of a collapsing star via fully dynamical approach. We derive and simplify the complete dynamical equation system for a collapsing spherically symmetrical star with perfect fluid, and establish some new constraints on the initial and boundary conditions. The mass density near the center can be approxi...

In this letter we show that, abundant contents in the energy momentum tensor were overlooked and simply merged into the energy density $\rho$ and pressure $P$. They are interactive potentials with different properties from that of $\rho$ and $P$, which can be used as fingerprints for different interaction. In the usual treatment for particles movin...

If there is a null gradient field in a 1+3 dimensional Lorentzian manifold, we can establish a kind of light-cone coordinate system for the manifold from the null gradient field. In such coordinate system, the metric takes a wonderful canonical form, which is much helpful for resolving the Einstein's field equation. In this paper, we show how to co...

In this paper, we discuss the system of Friedman–Robertson–Walker (FRW) metric coupling with massive nonlinear dark spinors in detail, where the thermodynamic movement of spinors is also taken into account. The results show that, the nonlinear potential of the spinor field can provide a tiny negative pressure, which resists the universe to become s...

In this paper, the author presents a framework for getting a series of exact vacuum solutions to the Einstein equation. This procedure of resolution is based on a canonical form of the metric. According to this procedure, the Einstein equation can be reduced to some 2-dimensional Laplace-like equations or rotation and divergence equations, which ar...

在宇宙学中，宇宙曲率 K 和宇宙学常数Λ是两个最重要的参数，其值对宇宙的演化有重大的影 响。本文在正能量密度和负初始压力的合理假设下，通过定性分析宇宙尺度因子与参数之间的动态关系， 发现宇宙的初始奇点是不可达的，K=1, 0 ≤ Λ < ͳ 0െ 吸ᷓlyെ 吸。这意味着，最初的大爆炸是不可能发生的，宇 宙的空间结构应该是三维球面ܵ ͵ ，宇宙的演化在时间上应该是循环的，宇宙学常数应为零或很小的量。由 于证明过程是非常简单明确的，前提条件也都是公认的事实，因此这些逻辑结论应该是相当可靠的。显然， 这些结论将有助于纠正一些流行的误解，并为进一步研究宇宙学中的其他问题如暗物质和暗能量的性质带 来极大方便。从某种意义上讲，我们恢复了赫拉克利特的古老信念：“世界，这个万物的实体，既不是由神 也不是由...

Some solutions to the anomalies of ultra high energy cosmic-ray(UHECR) and TeV $\gamma$-rays require disturbed non-quadratic dispersion relations, which suggest the Lorentz violation. Also, some new theories such as quantum gravity, string theory and the standard model extension imply the Lorentz violation. In this paper, we derive some transformat...

The equation of state and the state functions for the gravitational source are necessary conditions for solving cosmological model and stellar structure. The usual treatments are directly based on the laws of thermodynamics, and the physical meanings of some concepts are obscure. This letter show that, we can actually derive all explicit fundamenta...

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 c...

How to effectively solve the eigen solutions of the nonlinear spinor field equation coupling with some other interaction fields is important to understand the behavior of the elementary particles. In this paper, we derive a simplified form of the eigen equation of the nonlinear spinor, and then propose a scheme to solve their numerical solutions. T...

In this paper, we propose a new approach to the relativistic quantum mechanics for many-body, which is a self-consistent system constructed by juxtaposed but mutually coupled nonlinear Dirac's equations. The classical approximation of this approach provides the exact Newtonian dynamics for many-body, and the nonrelativistic approximation gives the...

The conventional method to determine the cosmic curvature is to measure the total mass density $\Omega_{\rm tot}$. Unfortunately the observational $\Omega_{\rm tot}$ is closely near the critical value 1. The computation of this paper shows that $\Omega_{\rm tot}\approx 1$ is an inevitable result for the young universe independent of the spatial top...

The nonlinear spinor fields coupled with the interactive potentials are important in the theory of elementary particles. In this paper, we establish the relationship between field theory and corresponding classical mechanics, and derive the local Lorentz transformations for the classical parameters. The classical mass of a particle is clearly defin...

The accelerating expansion of the present Universe is an exciting challenge to the standard cosmology, which reflects that our current theories on matter have some incompletion. In this paper, we analyze the cosmological model with nonlinear spinor fields source in detail. The results may be able to provide a natural explanation for the puzzles of...

In order to study the dynamical behavior of the coupling system of the space-time and Fermions, the explicit form of the energy-momentum tensor of the spinors in curved space-time is wanted. The energy-momentum tensor is closely related to the vierbien formalism, which can not be uniquely determined by the metric. This flexibility increases difficu...

Calculating the spinor connection in curved spacetime is a tiresome and fal-lible task. This pedagogical paper display an equivalent but simple form of the covariant derivative for both the Weyl spinor and the Dirac bispinor, which is more convenient for calculation, and its geometrical meanings are more distinct. We separate the spinor connection...

The vierbien formalism can not be uniquely determined by the metric. This flexibility increases difficulties in studing their relation and properties, and eas-ily leads to ambiguous results. Considering the importance of the interaction between spinor fields and the spacetime, in this paper we derive some explicit expressions for vierbien formalism...

In this paper, we restudy the Green function expressions of field equations. We derive the explicit form of the Green functions for the Klein-Gordon equation and Dirac equation, and then estimate the decay rate of the solution to the linear equations. The main motivation of this paper is to show that: (1). The formal solutions of field equations ex...

In this paper, we solve the particle-like eigenstates of a class of nonlinear dark spinor equation, and compute several functions which reflect its characteristics. The numerical results show that, the nonlinear spinor equation has only finite meaningful eigenstates, which have only positive discrete mass spectrum. The ground state of the dark spin...