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Visualization of eEDM and AEDM. The eEDM vector is aligned along the angular momentum vector. Its dipole is a static charge shift with respect to the center of mass. The orientation of the AEDM vector is independent from the angular momentum. Its dipole is a dynamic charge shift with respect to the stationary center of mass. The eEDM vector is collinear with the angular momentum vector ħ. Its static dipole moment is non-zero. The AEDM vector is collinear with the position vector ħ/c. Its static dipole moment is zero. Note that the finite dimensions of the AEDM may shrink to zero while preserving a finite dynamic dipole moment value. An eEDM is not consistent with a pointlike structure, while the AEDM is, because of the Heisenberg uncertainty
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An analysis is presented of the possible existence of the second anomalous dipole moment of Dirac’s particle next to the one associated with the angular momentum. It includes a discussion why, in spite of his own derivation, Dirac has doubted about its relevancy. It is shown why since then it has been overlooked and why it has vanished from leading...
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Citations
... The vertical one is the equivalent of the magnetic dipole moment of an electron. The (real valued) horizontal dipole moment is the equivalent of the (imaginary valued) electric dipole moment of an electron [9,10]. In a later description, after recognizing that this structure shows properties that match with a Maxwellian description, the quarks have been described as magnetic monopoles in Comay's Regular Charge Monopole Theory (RCMT) [7,11]. ...
... Playing with Dirac's gamma matrices revealed the possible existence of a real valued second dipole moment. It is a recent result, published in 2020 [9] and updated somewhat later [10]. It met some opposition because it violates the Lorentz invariance. ...
... Moreover, it is a Dirac particle that gains a constituent mass by interaction with fields from other sources. Although Maxwellian, the particle may have two real dipole moments, instead of a single real one next to an imaginary one such as shown by Dirac particles of the electron-type [8][9][10]. In this article it has been shown that the archetype meson, the pion, flips the state the antiparticle into the particle state, thereby producing a structure with two kernels, while preserving a configuration in which the repulsive force between the kernels is balanced with the attractive force of the quark's real second dipole moment. ...
A structure based analysis of the pion’s decay path reveals that neutrinos can show up in three eigenstates. It requires a proper understanding of the nature of charged leptons, such as why the loss of binding energy stops the lepton generation at the tauon level. The analysis quantifies this binding energy in terms of the weak interaction strength as embodied by the weak interaction boson and the strength of the energetic background field as embodied by the Higgs boson. Next to this it is shown that a reconstruction of Fermi’s neutrino theory allows a quantitative assessment of the Fermi constant straightforwardly from the weak interaction strength. The article ends with the conclusion that neutrino oscillation is not a physical phenomenon, but, instead, a measurement interpretation induced from projecting the statistical behaviour of a multi-particle ensemble onto a single particle.
... The vertical one is the equivalent of the magnetic dipole moment of an electron. The (real valued) horizontal dipole moment is the equivalent of the (imaginary valued) electric dipole moment of an electron [8,9]. In a later description, after recognizing that this structure shows properties that match with a Maxwellian description, the quarks have been described as magnetic monopoles in Comay's Regular Charge Monopole Theory (RCMT) [10]. ...
... Playing with Dirac's gamma matrices revealed the possible existence of a real valued second dipole moment. It is a recent result, published in 2020 [8] and updated somewhat later [9]. It met some opposition because it violates the Lorentz invariance. ...
... Moreover, it is a Dirac particle that gains a constituent mass by interaction with fields from other sources. Although Maxwellian, the particle may have two real dipole moments, instead of a single real one next to an imaginary one such as shown by Dirac particles of the electron-type [8,22]. In this article it has been shown that the archetype meson, the pion, flips the spin of one of its constituents thereby producing a structure with two kernels, while preserving a configuration in which the repulsive force between the kernels is balanced with the attractive force of the quark's real second dipole moment. ...
A structure based analysis of the pion’s decay path reveals that neutrinos can show up in three eigenstates. It requires a proper understanding of the nature of charged leptons, such as why the loss of binding energy stops the lepton generation at the tauon level. The analysis quantifies this binding energy in terms of the weak interaction strength as embodied by the weak interaction boson and the strength of the energetic background field as embodied by the Higgs boson. Next to this it is shown that a reconstruction of Fermi’s neutrino theory allows a quantitative assessment of the Fermi constant straightforwardly from the weak interaction strength. The article ends with the conclusion that neutrino oscillation is not a physical phenomenon, but, instead, a measurement interpretation induced from projecting the statistical behaviour of a multi-particle ensemble onto a single particle.
... while for quarks [5,8], ...
... This is different for a quark. Unlike an electron, the quark, subject to the gamma constraints (3), shows two real dipole moments [8,9]. This is proven once more in Appendix C. Hence, in qualitative terms, the potential field of a quark along the axis of the polarisable dipole, can be expressed as, ...
... Because it has similar properties as particle spin and because particle spin is related with the quark's intrinsic (anomalous) angular dipole moment h, one may expect that isospin is related with the quark's (anomalous) intrinsic linear dipole moment h/c. As discussed in paragraph 2, this property has remained unknown up to its description in 2021 [8,9]. However, whereas the particle spin state allows a direct interpretation as the spatial orientation of the intrinsic angular dipole moment, the spatial orientation of the intrinsic linear dipole moment is structurally bound. ...
The mass of the nucleons is calculated from first principles by defining the quark as a non-gravitational particle, subject to Dirac’s equation with non-canonical gamma matrices. Unlike the canonical electron-type, this Dirac particle has two real dipole moments, which allows a structural modelling of hadrons. It is shown how such modelling reveals striking correspondences and differences between dually related particles and properties like electrons and quarks, photons and gluons, pions and nucleons, spin and isospin and protons and neutrons. It is a stepping stone to the actual calculation, which competes in precision with lattice QCD. The appendix contains a Lorentz covariance proof of hadrons composed by such particular Dirac-type quarks.
... The Dirac equation [1,2] has been extensively explored across a wide range of scientific disciplines, demonstrating its significant relevance and broad applicability. Its investigations encompass various topics, including the Dirac oscillator [3,4], charged particles in static electromagnetic fields [5], pseudospin symmetry of nucleons in relativistic Manning-Rosen potentials [6], the behavior of Dirac particles in curved spacetimes [7][8][9], the Lorentzand CPT-violating standard model extension [10][11][12][13][14][15], electronic properties [16,17], topological defects of graphene [18], quantum rings [19], cosmic string spacetimes [20], and others [21][22][23][24][25][26][27]. These comprehensive investigations collectively contribute to the enhanced understanding of the implications and applications of the Dirac equation in modern physics. ...
... Moreover, recent developments in the literature have unveiled connections between the AA phase and other phenomena, such as topological phases of matter and supersymmetry [51]. Now, we evaluate the phases the Aharonov-Anandan (AA) geometrical phase developed by the spinor [19,26], which is given by: ...
This paper explores the relativistic behavior of spin--half particles possessing an Electric Dipole Moment (EDM) in a curved spacetime background induced by a spiral dislocation. A thorough review of the mathematical formulation of the Dirac spinor in the framework of quantum field theory sets the foundation for our investigation. By deriving the action that governs the interaction between the spinor field, the background spacetime, and an external electric field, we establish a framework to study the dynamics of the system. Solving the resulting wave equation reveals a set of coupled equations for the radial components of the Dirac spinor, which give rise to a modified energy spectrum attributed to the EDM. To validate our findings, we apply them to the geometric phase and thermodynamics.
... The vertical one is the equivalent of the magnetic dipole moment of an electron. The (real valued) horizontal dipole moment is the equivalent of the (imaginary valued) electric dipole moment of an electron [11,12 . Hypothetical equivalence of the quark's polarisable linear dipole moment with the magnetic dipole moment of its electric charge attribute. ...
... The vertical one is the equivalent of the magnetic dipole moment of an electron. The (real valued) horizontal dipole moment is dipole moment of an electron [11,12]. ...
Starting from an overview of neutrino problems and a simplified survey of Fermi’s neutrino theory, it is shown why neutrinos are left-handed and why they seem to show an oscillatory behaviour between their flavours. After addressing the question how to assess the naked mass of the true elementary particles, it is hypothesized that the elementary constituents of the nuclear background energy and the cosmological background energy are the same. This allows to derive the magnitude of the quark’s “naked” mass from the polarization of the vacuum.
... Over the past decades, the Dirac equation [1] has been studied in various subjects and fields of physics. For example, one can refer to study the Dirac oscillator [2,3], a charged Dirac particle in a static electromagnetic field [4], the Pseudospin symmetry of a Dirac nucleon in the relativistic Manning-Rosen potential [5], the Dirac particle in the curved space-time [6][7][8], the Dirac particle in the framework of the Lorentz-and CPT-violating standard-model extension [9][10][11][12][13][14], the electronic properties of graphene obtained from a Dirac Hamiltonian for a massless fermion [15,16], relativistic quantum dynamics of a Dirac particle confined in a quantum ring [17], the influence of dislocations, as a kind of topological defects in graphene, on the electronic properties of a Dirac particle [18], the Dirac particle in a chiral cosmic string space-time [19], the Dirac particle with arbitrary magnetic moment [20], bound-state dynamics of a neutron with an anomalous magnetic dipole moment interacting with certain external fields [21,22], bound states and geometric quantum phases for the Dirac particle with a magnetic dipole moment in a cosmic string space-time [23,24], on the second dipole moment of Dirac particle [25], and the developed form of particle-wave duality based on Einstein's geodesic equation in two-dimensional space-time versus the Dirac result [26]. ...
In this paper, we study the relativistic quantum dynamics of a neutral Dirac particle with a permanent magnetic dipole moment that interacts with an external magnetic field in the background space-time of a linear topological defect called spiral dislocation. The generalized Dirac wave equation is derived from the full action of that model involving the Lagrangian density of the Dirac spinor field in the background and the interaction model. The energy eigenvalues and corresponding wave functions are found in closed form by reducing the problem to that of a non-relativistic particle moving freely on a plane with a hole at the origin whose radius is determined by the defect parameter. In the limit of vanishing external magnetic field we are also able to establish a hidden SUSY structure of the underlying Dirac Hamiltonian allowing us to discuss the non-relativistic limit in some detail.
... The vertical one is the equivalent of the magnetic dipole moment of an electron. The (real valued) horizontal dipole moment is the equivalent of the (imaginary valued) electric dipole moment of an electron [7,8]. In a later description, after recognizing that this structure shows properties that match with a Maxwellian description, the quarks have been described as magnetic monopoles in Comay's Regular Charge Monopole Theory (RCMT). ...
... Electron energy distribution from neutron beta decay, calculated and experimental (dots).. Source: ref.[5,7]. ...
A structure based analysis of the pion’s decay path reveals that neutrinos can show up in three eigenstates. It requires a proper understanding of the nature of charged leptons, such as why the loss of binding energy stops the lepton generation at the tauon level. The analysis quantifies this binding energy in terms of the weak interaction strength as embodied by the weak interaction boson and the strength of the energetic background field as embodied by the Higgs boson. Next to this it is shown that a reconstruction of Fermi’s neutrino theory allows a quantitative assessment of the Fermi constant straightforwardly from the weak interaction strength. The article ends with the conclusion that neutrino oscillation is not a physical phenomenon, but, instead, a measurement interpretation induced from projecting the statistical behaviour of a multi-particle ensemble onto a single particle.
... . Therein ) (t U is the step function of Heaviside. It has the value zero for t 0 and is equal to 1 for t 0. The pointlike character of the particle is expressed by a Dirac pulse that has the value 1 for = r 0 and the value zero 5 for r 0 . The wave equation is the relation from which the energy value can be determined at any time and in any place, assuming that the space is empty, i.e. contains no fields, and is spherically isotropic. ...
In an historic perspective on the development of the Standard Model of particle physics it is shown how mathematically driven axioms have masked the merits of a physically comprehensible structural view. It is concluded that the difference between the two approaches can be traced back to two major issues. Whereas in the Standard Model the quark is a Dirac particle with a single real dipole moment, the quark in the structural model, in confinement with other quarks, is a Dirac particle with two real dipole moments. The second issue is the view that empty space does not exist, but that space is filled with a polarisable energetic fluid. It is shown how recognition of these two issues pave a road to reconcile particle physics with gravity, in which the quark can be seen as a magnetic electron and in which the gluon, as the strong force carrier, can be seen as a massive photon.
... , gives [2,7], ...
... About the second item he remarked that he doubted about the physical meaning of an imaginary electrical dipole moment. Curiously, like proven in [7] and in its update [8], a different set of matrices may turn the imaginary electrical dipole moment into a real one. ...
... Note also that the temporal parameter is written as proper time to emphasize the (special) relativistic nature of Dirac's equation in free space. Rewriting (7) in the Weyl format gives, ...
In this article the possible impact on the present state of particle physics theory is discussed of two unrecognized theoretical elements. These elements are the awareness that (a) the quark is a Dirac particle with a polarisable dipole moment in a scalar field and that (b) Dirac’s wave equation for fermions, if derived from Einstein’s geodesic equation, reveals a scaling theorem for quarks. It is shown that recognition of these elements proves by theory quite some relationships that are up to now only empirically assessed, such as for instance, the mass relationships between the elementary quarks, the relationship between the bare mass and the constituent mass of quarks, the mass spectrum of hadrons and the mass values of the Z boson and the Higgs boson.
... This is different for a quark. Unlike an electron, the quark, subject to the gamma constraints (3), shows two real dipole moments [8,9]. Hence, in qualitative terms, the potential field of a quark along the axis of the polarisable dipole, can be expressed as, ...
... In the standard model of particle physics, this isospin is property of the quark without a known physical interpretation. Because it has similar properties as nuclear spin and because nuclear spin is related with the quark's angular dipole moment ħ, one may expect that isospin is related with the qua As discussed in paragraph 2, this property has remained unknown up t 2021 [7,8]. However, whereas the nuclear spin state allows a direct interpretation as the spatial orientation of the angular dipole mom moment is structurally bound. ...
... It has already been concluded at the end of paragraphs 5 and 7 that the capabilities to calculate the masses of the nucleons and the mass difference between a proton and a neutron on the basis of a rather simple structural model have a similar accuracy as those claimed from lattice QCD. This article is a summary, application and extension of previous work [5,8,9,11,12,16]. It is based upon a somewhat different view on quarks as compared to canonical theory. ...
The mass of the nucleons is calculated from first principles by defining the quark as a non-gravitational particle, subject to Dirac’s equation with non-canonical gamma matrices. Unlike the canonical electron-type, this Dirac particle has two real dipole moments, which allows a structural modelling of hadrons. It is shown how such modelling reveals striking correspondences and differences between dually related particles and properties like electrons and quarks, photons and gluons, pions and nucleons, spin and isospin and protons and neutrons. It is a stepping stone to the actual calculation, which competes in precision with lattice QCD. The appendix contains a Lorentz covariance proof of hadrons composed by such particular Dirac-type quarks.
