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A Derivation of the Ricci Flow

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Journal of Applied Mathematics and Physics 2021年第9期9卷 2179-2186页

作者： Vu B. ho 9 adela Court Mulgrave Australia

In this work, we show that by restricting to the subgroup of time-independent coordinate transformations, then it is possible to derive the Ricci flow from the Bianchi identities. To achieve this, we first show that the field equations of the gravitational field, the Newton’s second law of classical dynamics, and the Maxwell field equations of the electromagnetic field all share the same mathematical structure. Consequently, the Ricci flow itself may be regarded as dynamical equations used to describe physical processes associated with the gravitational field, such as the process of smoothing out irregularities of distribution of matter in space.

关键词： Ricci Flow Bianchi Identities General Relativity Classical Physics

On the Field Equations of General Relativity

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Journal of Applied Mathematics and Physics 2022年第1期10卷 49-55页

作者： Vu B. ho 9 adela Court Mulgrave Australia

In this work, we examine the geometric character of the field equations of general relativity and propose to formulate relativistic field equations in terms of the Riemann curvature tensor. The resulted relativistic field equations are also integrated into the general framework that we have presented in our previous works that all known classical fields can be expressed in the same dynamical form. We also discuss a possibility to reformulate the field equations of general relativity so that the Ricci curvature tensor and the energy-momentum tensor can appear symmetrically in the field equations without violating the conservation law stated by the covariant derivative.

关键词： General Relativity Classical Field Equations Riemann Curvature Tensor

Molecular Structure of Atomic Nucleus

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Journal of Modern Physics 2020年第9期11卷 1395-1409页

作者： Vu B. ho Advanced Study 9 Adela Court Mulgrave Victoria Australia

In this work, we extend our work on the Heisenberg model of the neutron formulated as a dwarf hydrogen-like atom under the influence of the More General Exponential Screened Coulomb Potential (MGESCP) to show that an atomic nucleus may possess a molecular structure made up of atoms bonding together by a potential used to describe the strong force associated with a generalised Yukawa MGESCP potential. We show that the neutrons and protons are arranged into narrow lattices therefore they may fold to form three-dimensional shells by bonding similar to hydrogen bonding. In particular, the nucleons may form stable structures such as that of fullerenes in which the vertices are occupied by the nucleons which are simply just protons. For example, a nucleus with a total number of 60 nucleons may arrange itself into the topological structure of a buckminsterfullerene. We also apply Schrödinger wave equation with central field approximation to describe the quantum dynamics of nuclei of atomic atoms that now possess the physical structure of a dwarf molecular ion.

关键词： Heisenberg Model of the Neutron Dwarf Hydrogen Atom Molecular Structure of Atomic Nucleus Weak and Strong Interactions Yukawa MGESCP Potential Fullerene

A Reformulation of Newton Second Law for Charged Particles and Its Application to Quantum Dynamics

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Journal of Applied Mathematics and Physics 2021年第11期9卷 2796-2806页

作者： Vu B. ho 9 adela Court Mulgrave Australia

We propose a reformulation of Newton’s second law of motion for charged particles and possible applications of the reformulation to quantum dynamics. We show that the negative energy states arising from the Dirac equation in relativistic quantum mechanics can be verified using the reformulating framework. We also discuss possible hidden dynamics underlying the concept of quantum jumps in quantum mechanics as outlined in Schrödinger’s article: ARE THERE QUANTUM JUMPS? In this case, we show that the hidden dynamics of quantum jumps are also determined by the Coulomb interaction between charged particles.

关键词： Reformulation of Newton Second Law Dirac Negative Energy States Quantum Jumps in Quantum Mechanics

A Quantum Dynamics of Heisenberg Model of the Neutron Associated with Beta Decay

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Journal of Modern Physics 2019年第9期10卷 1065-1082页

作者： Vu B. ho Advanced Study 9 Adela Court Mulgrave Australia

In this work we re-examine a model of the nucleons that involve the weak interaction which was once considered by Heisenberg;that is a neutron may have the structure of a dwarf hydrogen-like atom. We formulate a quantum dynamics for the Heisenberg model of the neutron associated with interaction that involves the beta decay in terms of a mixed Coulomb-Yukawa potential and the More General Exponential Screened Coulomb Potential (MGESCP), which has been studied and applied to various fields of physics. We show that all the components that form the MGESCP potential can be derived from a general system of linear first order partial differential equations similar to Dirac relativistic equation in quantum mechanics. There are many interesting features that emerge from the MGESCP potential, such as the MGESCP potential can be reduced to the potential that has been proposed to describe the interaction between the quarks for strong force in particle physics, and the energy spectrum of the bound states of the dwarf hydrogen-like atom is continuous with respect to distance. This result leads to an unexpected implication that a proton and an electron may also interact strongly at short distances. We also show that the Yukawa potential when restrained can generate and determine the mathematical structures of fundamental particles associated with the strong and weak fields.

关键词： Quantum Dynamics Beta Decay Weak and Strong Interactions Dirac Equations Coulomb Potential Yukawa Potential MGESCP Potential Differential Equations

Fluid State of Dirac Quantum Particles

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Journal of Modern Physics 2018年第14期9卷 2402-2419页

作者： Vu B. ho Advanced Study 9 Adela Court Mulgrave Victoria Australia

In our previous works, we suggest that quantum particles are composite physical objects endowed with the geometric and topological structures of their corresponding differentiable manifolds that would allow them to imitate and adapt to physical environments. In this work, we show that Dirac equation in fact describes quantum particles as composite structures that are in a fluid state in which the components of the wavefunction can be identified with the stream function and the velocity potential of a potential flow formulated in the theory of classical fluids. We also show that Dirac quantum particles can manifest as standing waves which are the result of the superposition of two fluid flows moving in opposite directions. however, for a steady motion a Dirac quantum particle does not exhibit a wave motion even though it has the potential to establish a wave within its physical structure, therefore, without an external disturbance a Dirac quantum particle may be considered as a classical particle defined in classical physics. And furthermore, from the fact that there are two identical fluid flows in opposite directions within their physical structures, the fluid state model of Dirac quantum particles can be used to explain why fermions are spin-half particles.

关键词： Dirac Equation Wave Mechanics Stan Fluid Mechanics Stream Function Velocity Potential Potential Flow General Relativity Maxwell Field Equations CW Complexes Differential Geometry Topology Differentiable Manifolds Topological Transformation

Classification of Relativity

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Journal of Modern Physics 2020年第4期11卷 535-564页

作者： Vu B. ho Advanced Study 9 Adela Court Mulgrave Victoria Australia

In this work, we discuss the possibility to classify relativity in accordance with the classification of second order partial differential equations that have been applied into the formulation of physical laws in physics. In mathematics, since second order partial differential equations can be classified into hyperbolic, elliptic or parabolic type, therefore we show that it is also possible to classify relativity accordingly into hyperbolic, elliptic or parabolic type by establishing coordinate transformations that preserve the forms of these second order partial differential equations. The coordinate transformation that preserves the form of the hyperbolic equation is the Lorentz transformation and the associated space is the hyperbolic, or pseudo-Euclidean, relativistic spacetime. Typical equations in physics that comply with hyperbolic relativity are Maxwell and Dirac equations. The coordinate transformation that preserves the form of the elliptic equation is the modified Lorentz transformation that we have formulated in our work on Euclidean relativity and the associated space is the elliptic, or Euclidean, relativistic spacetime. As we will show in this work, equations that comply with elliptic relativity are the equations that describe the subfields of Maxwell and Dirac field. And the coordinate transformation that preserves the form of the parabolic equation is the Euclidean transformation consisting of the translation and rotation in the spatial space and the associated space is the parabolic relativistic spacetime, which is a Euclidean space with a universal time. Typical equations in physics that comply with parabolic relativity are the diffusion equation, the Schrödinger equation and in particular the diffusion equations that are derived from the four-current defined in terms of the differentiable structures of the spacetime manifold, and the Ricci flow.

关键词： Special Relativity Elliptic Equation Hyperbolic Equation Parabolic Equation Elliptic Relativity Hyperbolic Relativity Parabolic Relativity Classification of Relativity Maxwell and Dirac Field Maxwell and Dirac Subfield

A Topological Transformation of Quantum Dynamics

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Journal of Modern Physics 2019年第2期10卷 102-127页

作者： Vu B.ho Advanced Study 9 Adela CourtMulgraveAustralia

In this work, we discuss the topological transformation of quantum dynamics by showing the wave dynamics of a quantum particle on different types of topological structures in various dimensions from the fundamental polygons of the corresponding universal covering spaces. This is not the view from different perspectives of an observer who simply uses different coordinate systems to describe the same physical phenomenon but rather possible geometric and topological structures that quantum particles are endowed with when they are identified with differentiable manifolds that are embedded or immersed in Euclidean spaces of higher dimension. We present our discussions in the form of Bohr model in one, two and three dimensions using linear wave equations. In one dimension, the fundamental polygon is an interval and the universal covering space is the straight line and in this case the standing wave on a finite string is transformed into the standing wave on a circle which can be applied into the Bohr model of the hydrogen atom. In two dimensions, the fundamental polygon is a square and the universal covering space is the plane and in this case, the standing wave on the square is transformed into the standing wave on different surfaces that can be formed by gluing opposite sides of the square, which include a 2-sphere, a 2-torus, a Klein bottle and a projective plane. In three dimensions, the fundamental polygon is a cube and the universal covering space is the three-dimensional Euclidean space. It is shown that a 3-torus and the manifold K?× S1?defined as the product of a Klein bottle and a circle can be constructed by gluing opposite faces of a cube. Therefore, in three-dimensions, the standing wave on a cube is transformed into the standing wave on a 3-torus or on the manifold K?× S1. We also suggest that the mathematical degeneracy may play an important role in quantum dynamics and be associated with the concept of wavefunction collapse in quantum mechanics.

关键词： Quantum Topology Topological Transformation Quantum Dynamics Differentiable Geometry and Topology Differentiable Manifolds Schrodinger Wave Mechanics Bohr Model in One Two and Three Dimensions de Broglie Wave-Particle Duality

A Formulation of Spin Dynamics Using Schrodinger Equation

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Journal of Modern Physics 2019年第11期10卷 1374-1393页

作者： Vu B.ho Advanced Study 9 Adela CourtMulgraveAustralia

In quantum mechanics, there is a profound distinction between orbital angular momentum and spin angular momentum in which the former can be associated with the motion of a physical object in space but the latter cannot. The difference leads to a radical deviation in the formulation of their corresponding dynamics in which an orbital angular momentum can be described by using a coordinate system but a spin angular momentum cannot. In this work, we show that it is possible to treat spin angular momentum in the same manner as orbital angular momentum by formulating spin dynamics using Schrödinger equation in an intrinsic coordinate system. As an illustration, we apply the formulation to the dynamics of a hydrogen atom and show that the intrinsic spin angular momentum of the electron can take half-integral values and, in particular, the intrinsic mass of the electron can take negative values. We also consider a further extension by generalising the formulation so that it can be used to describe other intrinsic dynamics that may associate with a quantum particle, for example, when a hydrogen atom radiates a photon, the photon associated with the electron may also possess an intrinsic dynamics that can be described by an intrinsic wave equation that has a similar form to that for the electron.

关键词： Spin Angular Momentum Spin Dynamics Orbital Angular Momentum Schrodinger Equation Half-Integer Values Intrinsic Coordinate Systems Negative Mass