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 me...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.展开更多
An intriguing quasi-relativistic wave equation, which is useful between the range of applications of the Schr<span style="white-space:nowrap;">ö</span>dinger and the Klein-Gordon equatio...An intriguing quasi-relativistic wave equation, which is useful between the range of applications of the Schr<span style="white-space:nowrap;">ö</span>dinger 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.展开更多
In this treatise we stress the analogy between strongly interacting many-body systems and elementary particle physics in the context of Quantum Field Theory (QFT). The common denominator between these two branches of ...In this treatise we stress the analogy between strongly interacting many-body systems and elementary particle physics in the context of Quantum Field Theory (QFT). The common denominator between these two branches of theoretical physics is the Green’s function or propagator, which is the key for solving specific problems. Here we are concentrating on the vacuum, its excitations and its interaction with electron and photon fields.展开更多
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<span style="white-space:nowra...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<span style="white-space:nowrap;">?</span>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.展开更多
Using a novel wave equation, which is Galileo invariant but can give precise results up to energies<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style=&...Using a novel wave equation, which is Galileo invariant but can give precise results up to energies<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> as high as </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><i><span style="font-family:Verdana;">mc</span></i></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><sup>2</sup></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">, 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 Schr</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="line-height:102%;font-family:Verdana;"><span style="white-space:nowrap;">ö</span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">dinger equation.</span></span></span>展开更多
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 st...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 (m<sub>P</sub>), or with the absolute value of the charge larger than the Plank charge (q<sub>P</sub>). It is proposed the existence of primordial antimatter electrical sinks. It is also suggested that all macroscopic matter objects with a mass m > m<sub>P</sub>, and all macroscopic antimatter bodies with a charge |q| > q<sub>P</sub> 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.展开更多
We present sixteen-component values “sedeons”, generating associative non-commutative space-time algebra. The generalized relativistic wave equations based on sedeonic wave function and space-time operators are prop...We present sixteen-component values “sedeons”, generating associative non-commutative space-time algebra. The generalized relativistic wave equations based on sedeonic wave function and space-time operators are proposed. We demonstrate that sedeonic second-order wave equation for massive field can be reformulated as the quasi-classical equation for the potentials of the field or in equivalent form as the Maxwell-like equations for the field intensities. The sedeonic first-order Dirac-like equations for massive and massless fields are also discussed.展开更多
We present an alternative sixteen-component hypercomplex scalar-vector values named “space-time sedenions”, generating associative noncommutative space-time Clifford algebra. The generalization of relativistic quant...We present an alternative sixteen-component hypercomplex scalar-vector values named “space-time sedenions”, generating associative noncommutative space-time Clifford algebra. The generalization of relativistic quantum mechanics and field theory equations based on sedenionic wave function and space-time operators is discussed.展开更多
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 wa...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.展开更多
We generalize relativistic quantum mechanics and the Standard Model of elementary particle physics by considering a finite limit for the smallest measurable length. The resulting theory of Space-Time Quantization is l...We generalize relativistic quantum mechanics and the Standard Model of elementary particle physics by considering a finite limit for the smallest measurable length. The resulting theory of Space-Time Quantization is logically consistent and accounts for all possible particle states by means of four new quantum numbers. They specify possible variations of wave functions at the smallest possible scale in space and time, while states of motion are defined by their large-scale variations. This theory also provides insight into the nature and properties of dark matter particles. It can facilitate their detection and identification because of a very strict conservation law.展开更多
文摘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.
文摘An intriguing quasi-relativistic wave equation, which is useful between the range of applications of the Schr<span style="white-space:nowrap;">ö</span>dinger 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.
文摘In this treatise we stress the analogy between strongly interacting many-body systems and elementary particle physics in the context of Quantum Field Theory (QFT). The common denominator between these two branches of theoretical physics is the Green’s function or propagator, which is the key for solving specific problems. Here we are concentrating on the vacuum, its excitations and its interaction with electron and photon fields.
文摘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<span style="white-space:nowrap;">?</span>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.
文摘Using a novel wave equation, which is Galileo invariant but can give precise results up to energies<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> as high as </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><i><span style="font-family:Verdana;">mc</span></i></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><sup>2</sup></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">, 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 Schr</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="line-height:102%;font-family:Verdana;"><span style="white-space:nowrap;">ö</span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">dinger equation.</span></span></span>
文摘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 (m<sub>P</sub>), or with the absolute value of the charge larger than the Plank charge (q<sub>P</sub>). It is proposed the existence of primordial antimatter electrical sinks. It is also suggested that all macroscopic matter objects with a mass m > m<sub>P</sub>, and all macroscopic antimatter bodies with a charge |q| > q<sub>P</sub> 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.
文摘We present sixteen-component values “sedeons”, generating associative non-commutative space-time algebra. The generalized relativistic wave equations based on sedeonic wave function and space-time operators are proposed. We demonstrate that sedeonic second-order wave equation for massive field can be reformulated as the quasi-classical equation for the potentials of the field or in equivalent form as the Maxwell-like equations for the field intensities. The sedeonic first-order Dirac-like equations for massive and massless fields are also discussed.
文摘We present an alternative sixteen-component hypercomplex scalar-vector values named “space-time sedenions”, generating associative noncommutative space-time Clifford algebra. The generalization of relativistic quantum mechanics and field theory equations based on sedenionic wave function and space-time operators is discussed.
基金Supported by National Natural Science Foundation of China (10775148,10975146,11035006)
文摘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.
文摘We generalize relativistic quantum mechanics and the Standard Model of elementary particle physics by considering a finite limit for the smallest measurable length. The resulting theory of Space-Time Quantization is logically consistent and accounts for all possible particle states by means of four new quantum numbers. They specify possible variations of wave functions at the smallest possible scale in space and time, while states of motion are defined by their large-scale variations. This theory also provides insight into the nature and properties of dark matter particles. It can facilitate their detection and identification because of a very strict conservation law.