Relativistic Mechanics in Positive and Negative Subspace-Time according to the Inverse Relativity Model

In the second paper on the inverse relativity model, we explained in the first paper [1] that analyzing the four-dimensional displacement vector on space-time according to a certain approach leads to the splitting of space-time into positive and negative subspace-time. Here, in the second paper, we continue to analyze each of the four-dimensional vectors of velocity, acceleration, momentum, and forces on the total space-time fabric. According to the approach followed in the first paper. As a result, in the special case, we obtain new transformations for each of the velocity, acceleration, momentum, energy, and forces specific to each subspace-time, which are subject to the positive and negative modified Lorentz transformations described in the first paper. According to these transformations, momentum remains a conserved quantity in the positive subspace and increases in the negative subspace, while the relativistic total energy decreases in the positive subspace and increases in the negative subspace. In the general case, we also have new types of energy-momentum tensor, one for positive subspace-time and the other for negative subspace-time, where the energy density decreases in positive subspace-time and increases in negative subspace-time, and we also obtain new gravitational field equations for each subspace-time.

Direct Relativistic Extension of the Madelung-de-Broglie-Bohm Reformulations of Quantum Mechanics and Quantum Hydrodynamics

The basic equations of the non-relativistic quantum mechanics with trajectories and quantum hydrodynamics are extended to the relativistic domain. This is achieved by using a Schr?dinger-like equation, which describes a particle with mass and spin-0 and with the correct relativistic relation between its linear momentum and kinetic energy. Some simple but instructive free particle examples are discussed.

Hamilton-Jacobi and Lagrange Formulations of Relativistic Quantum Mechanics Wave Equations with Solutions with Only-Positive and Only-Negative Kinetic Energies

Using the Hamilton-Jacobi and the Lagrange formalisms, a pair of relativistic quantum mechanics equations are obtained by abduction. These equations, in contrast with the Klein-Gordon and other relativistic quantum mechanics equations, have no solutions with both positive and negative kinetic energies. The equation with solutions with only positive kinetic energy values describes a spin-0 particle of mass m, which is moving at relativistic speeds in a scalar potential. The wavefunctions and the energies corresponding to the associated antiparticle can be obtained by solving the other equation, which only has solutions with negative kinetic energy values.

Lie Symmetrical Hojman Conserved Quantity of Relativistic Mechanical System

In this paper, we study the Lie symmetrical Hojman conserved quantity of a relativistic mechanical system under general infinitesimal transformations of groups in which the time parameter is variable. The determining equation of Lie symmetry of the system is established. The theorem of the Lie symmetrical Hojman conserved quantity of the system is presented. The above results are generalization to Hojman's conclusions, in which the time parameter is not variable and the system is non-relativistic. An example is given to illustrate the application of the results in the last.

A Notable Quasi-Relativistic Wave Equation and Its Relation to the Schrödinger, Klein-Gordon, and Dirac Equations

An intriguing quasi-relativistic wave equation, which is useful between the range of applications of the Schrödinger and the Klein-Gordon equations, is discussed. This equation allows for a quantum description of a constant number of spin-0 particles moving at quasi-relativistic energies. It is shown how to obtain a Pauli-like version of this equation from the Dirac equation. This Pauli-like quasi-relativistic wave equation allows for a quantum description of a constant number of spin-1/2 particles moving at quasi-relativistic energies and interacting with an external electromagnetic field. In addition, it was found an excellent agreement between the energies of the electron in heavy Hydrogen-like atoms obtained using the Dirac equation, and the energies calculated using a perturbation approach based on the quasi-relativistic wave equation. Finally, it is argued that the notable quasi-relativistic wave equation discussed in this work provides interesting pedagogical opportunities for a fresh approach to the introduction to relativistic effects in introductory quantum mechanics courses.

Full relativistic calculations of the quadrupole and electric field gradients for C_2,N_2,and O_2

In the present work we calculate the energies,quadrupole moments,and electric field gradients（EFGs） of molecules C2,N2,and O2 based on the DIRRCI method with basis aug-cc-pVTZ-DK.We prove that the quadratic force constant k2 is the product of charge and EFG at its equilibrium nuclear distance.The dipole charge distributions for these symmetrical molecules are all in equilibrium,however,the quadrupole charge distributions are far from equilibrium;among these,there is the most remarkable deviation from equilibrium for N2,for its many charges concentrate on two sides of the molecule,which is in agreement with the well-known characteristic of the nitrogen molecule.The relativistic effect is remarkable even for the same period.

Quasi-Relativistic Description of Hydrogen-Like Atoms

Using a novel wave equation, which is Galileo invariant but can give precise results up to energies as high as mc2, exact quasi-relativistic quantum mechanical solutions are found for the Hydrogen atom. It is shown that the exact solutions of the Grave de Peralta equation include the relativistic correction to the non-relativistic kinetic energies calculated using the Schrödinger equation.

Natural Extension of the Schrodinger Equation to Quasi-Relativistic Speeds

A Schrödinger-like equation for a single free quantum particle is presented. It is argued that this equation can be considered a natural relativistic extension of the Schrödinger equation for energies smaller than the energy associated to the particle’s mass. Some basic properties of this equation: Galilean invariance, probability density, and relation to the Klein-Gordon equation are discussed. The scholastic value of the proposed Grave de Peralta equation is illustrated by finding precise quasi-relativistic solutions for the infinite rectangular well and the quantum rotor problems. Consequences of the non-linearity of the proposed equation for the quantum superposition principle are discussed.

On the Existence of a Minimum Universal Speed of Physical Transmissions Associated with Matter Wave in Special Relativity

In this work, we show that it is possible to establish coordinate transformations between inertial reference frames in the theory of special relativity with a minimum universal speed of physical transmissions. The established coordinate transformations, referred to as modified Lorentz transformations because they have almost identical form to the Lorentz transformations, also comply with the requirement of invariance of the Minkowski line element. Particularly, the minimum universal speed can be associated with the phase speed of de Broglie matter wave. As application, we also discuss the possibility to formulate relativistic classical and quantum mechanics for the special relativity associated with the modified Lorentz transformations, which describes physical processes that represent an expansion or a collapsing of massive quantum particles.

A study of transverse charge density of pions in relativistic quantum mechanics

The transverse charge density of pions is calculated based on relativistic quantum mechanics, where the pion is regarded as a quark-antiquark bound state. Corrections from the two spin-1/2 constituents and from the wave function of a quark and antiquark inside the bound system are discussed. The calculated results are compared to the results with a realistic effective Lagrangian approach as well as to that with a simple covariant model where the pion is regarded as a composite system with two scalar particles.

Broadband spectral fitting of blazars using XSPEC

The broadband spectral energy distribution（SED） of blazars is generally interpreted as radiation arising from synchrotron and inverse Compton mechanisms. Traditionally,the underlying source parameters responsible for these emission processes,like particle energy density,magnetic field,etc.,are obtained through simple visual reproduction of the observed fluxes. However,this procedure is incapable of providing confidence ranges for the estimated parameters. In this work,we propose an efficient algorithm to perform a statistical fit of the observed broadband spectrum of blazars using different emission models. Moreover,we use the observable quantities as the fit parameters,rather than the direct source parameters which govern the resultant SED. This significantly improves the convergence time and eliminates the uncertainty regarding initial guess parameters. This approach also has an added advantage of identifying the degenerate parameters,which can be removed by including more observable information and/or additional constraints. A computer code developed based on this algorithm is implemented as a user-defined routine in the standard X-ray spectral fitting package,XSPEC. Further,we demonstrate the efficacy of the algorithm by fitting the well sampled SED of blazar 3 C 279 during its gamma ray flare in 2014.

About the Observed Asymmetry between Matter and Antimatter

Some consequences, due to the existence of a pair of decoupled Schrödinger-like but relativistic quantum mechanics wave equations, are explored. It is shown that one equation directly describes the quantum states of a single spin-0 particle, and the other one indirectly describes the quantum states of the corresponding antiparticle. In correspondence with the matter-antimatter symmetry, for a Coulomb potential, a charge conjugation operation transforms the second equation in the first one. However, if a particle could interact with itself (gravitationally or electrically) due to the spread of its wavefunction, the C-symmetry could be broken;therefore, matter and antimatter could be distinguished. Under these assumptions, it is deducted the impossibility of the existence of particles and antiparticles with a mass larger than the Plank mass (mP), or with the absolute value of the charge larger than the Plank charge (qP). It is proposed the existence of primordial antimatter electrical sinks. It is also suggested that all macroscopic matter objects with a mass m > mP, and all macroscopic antimatter bodies with a charge |q| > qP should not be quantum but classical objects. It is argued that these findings could explain the absence of antimatter with a complicated structure and partially explain the excess of charged matter in the known Universe.

Quark Oscillation Causes Gravity

Quark movement is almost by the speed of light. Due to this speed their inertial mass-effect increases profoundly. That inertial effect is an accelerating force. Within the nucleon the force is the strong force. As quarks movements are back and forth movements, called zigzag or oscillating movements, there is movement in opposite directions. So the oppositely acting forces annihilate each other. However the force acting on objects receding from each other is a trifle stronger than that acting on objects approaching each other. This small difference between these forces is a “left over” force and “leaks” out of the nucleon. In previous manuscripts, formulae were presented to calculate these forces. In the present paper the “left over”, “leaking” force is estimated, and this force is gravity.

Semi-Relativistic Two-Body States of Spinless Particles with a Scalar-Type Interaction Potential

A semi-relativistic quantum approximation for mutual scalar interaction potentials is outlined and discussed.Equations are consistent with two-body Dirac equations for bound states of zero total angular momentum. Two-body effects near the non-relativistic limit for a linear scalar potential is studied in some detail.

Gravidynamics,spinodynamics and electrodynamics within the framework of gravitational quantum field theory

By noticing the fact that the charged leptons and quarks in the standard model are chirality-based Dirac spinors since their weak interaction violates maximally parity symmetry though they behave as Dirac fermions in electromagnetic interaction,we show that such a chirality-based Dirac spinor possesses not only electric charge gauge symmetry U(1)but also inhomogeneous spin gauge symmetry WS(1,3)=SP(1,3)?W1,3,which reveals the nature of gravity and spacetime.The gravitational force and spin gauge force are governed by the gauge symmetries W1,3and SP(1,3),respectively,and a biframe spacetime with globally fiat Minkowski spacetime as base spacetime and locally fiat gravigauge spacetime as a fiber is described by the gravigauge field through emergent non-commutative geometry.The gauge-geometry duality and renormalizability in gravitational quantum field theory(GQFT)are carefully discussed.A detailed analysis and systematic investigation on gravidynamics and spinodynamics as well as electrodynamics are carried out within the framework of GQFT.A full discussion on the generalized Dirac equation and Maxwell equation as well as Einstein equation and spin gauge equation is made in biframe spacetime.New effects of gravidynamics as extension of general relativity are particularly analyzed.All dynamic equations of basic fields are demonstrated to preserve the spin gauge covariance and general coordinate covariance due to the spin gauge symmetry and emergent general linear group symmetry GL(1,3,R),so they hold naturally in any spinning reference frame and motional reference frame.