Quantization Of Electric Charge Research Articles

Semi-classical description of electrostatics and quantization of electric charge

Abstract In this work, we present an explanation of the electric charge quantization based on a semi-classical model of electrostatic fields. We claim that in electrostatics, an electric charge must be equal to a rational multiple of the elementary charge of an electron. However, the charge is quantized if the system has certain boundary conditions that force the wavefunction representing an electric field to vanish at specific surfaces. Next, we develop the corresponding model for the electric displacement vector. It is demonstrated that a number of classical results, e.g. bending of field lines at the interface of two dielectric media, method of images, etc are all consistent with the predictions of this model. We also present the possible form of Gauss's law (or Poisson's equation), to find the wavefunctions of the field from a source charge distribution, in this model.

Weak charges quantization in SU(3)c ⊗ SU(n)L ⊗ U(1)Y gauge models

After proving, in a previous paper, that the electric charge quantization occurs as a natural consequence in renormalizable gauge models, we take here a step further within the same paradigm in order to obtain the precise weak charges quantization. To this end a viable boson mass spectrum is obtained first, once a proper parametrization in the Higgs sector is taken into consideration. Hence, by diagonalizing the neutral bosons mass matrix, the quantized neutral weak charge operators are obtained. The Standard Model phenomenology is not affected at all, as its scale (v SM = 246 GeV) is decoupled from the higher scale (V ∼ 10 TeV) specific to our generalized electro-weak unification.

Why Do Elementary Particles Have Such Strange Mass Ratios?—The Importance of Quantum Gravity at Low Energies

When gravity is quantum, the point structure of space-time should be replaced by a non-commutative geometry. This is true even for quantum gravity in the infra-red. Using the octonions as space-time coordinates, we construct pre-spacetime, pre-quantum Lagrangian dynamics. We show that the symmetries of this non-commutative space unify the standard model of particle physics with SU(2)R chiral gravity. The algebra of the octonionic space yields spinor states which can be identified with three generations of quarks and leptons. The geometry of the space implies quantisation of electric charge, and leads to a theoretical derivation of the mysterious mass ratios of quarks and the charged leptons. Quantum gravity is quantisation not only of the gravitational field, but also of the point structure of space-time.

Magnetic monopoles in two time dimensions

The observation of magnetic monopoles would lead to a symmetrization of Maxwell’s equations and provide explanations of fundamental properties such as the quantization of electric charge. Yet, in four dimensions, the covariant electromagnetic field tensor yields an action whose resulting field equations establish the absence of a magnetic charge. We here study the existence of magnetic monopoles in an extended space–time with a second time dimension, and construct the higher-dimensional gauge potential. This motivates the use of the Kalb–Ramond field, upon which a Kaluza–Klein-like reduction is performed under the assumption that the two time dimensions have no co-dependency. The resulting 5D electrodynamics contains a generalized version of Maxwell’s equations which contain magnetic charge densities whose source potential obeys a five-dimensional wave equation. As a second time dimension only acts on small length scales in the order of the Planck length, we provide a theory with symmetrized Maxwell’s equations including magnetic monopoles which do not violate current experimental evidence. We finally discuss the subsequent quantization of the electric charge as well as the weak interaction, equivalent to the violation of time reversal.

Maximally symmetric nonlinear extension of electrodynamics and charged particles

We consider couplings of electrically and magnetically charged sources to the maximally symmetric non-linear extension of Maxwell's theory called ModMax. The aim is to reveal physical effects which distinguish ModMax from Maxwell's electrodynamics. We find that, in contrast to generic models of non-linear electrodynamics, Lienard-Wiechert fields induced by a moving electric or magnetic particle, or a dyon are exact solutions of the ModMax equations of motion. We then study whether and how ModMax non-linearity affects properties of electromagnetic interactions of charged objects, in particular the Lorentz force, the Coulomb law, the Lienard-Wiechert fields, Dirac's and Schwinger's quantization of electric and magnetic charges, and the Compton Effect. In passing we also present an alternative form of the ModMax Lagrangian in terms of the coupling of Maxwell's theory to axion-dilaton-like auxiliary scalar fields which may be relevant for revealing the effective field theory origin of ModMax.

Monopoles from an Atmospheric Fixed Target Experiment.

Magnetic monopoles have a long history of theoretical predictions and experimental searches, carrying direct implications for fundamental concepts such as electric charge quantization. We analyze in detail for the first time magnetic monopole production from collisions of cosmic rays bombarding the atmosphere. This source of monopoles is independent of cosmology, has been active throughout Earth's history, and supplies an irreducible monopole flux for all terrestrial experiments. Using results for robust atmospheric fixed target experiment flux of monopoles, we systematically establish direct comparisons of previous ambient monopole searches with monopole searches at particle colliders and set leading limits on magnetic monopole production in the ∼5-100 TeV mass range.

Gauge Origin of Double Dark Parity and Implication for Dark Matter

Dark matter must be stabilized over the cosmological timescale, which demands the existence of a stabilizing symmetry, derived by a dark charge, $D$. The existence of this dark charge may affect the quantization of electric charge, which theoretically shifts the electric charge, thus the hypercharge to a novel gauge extension, $SU(3)_C\otimes SU(2)_L\otimes U(1)_Y\otimes U(1)_N$, where $N$ determines $D=T_3+N$, similar to $Q=T_3+Y$. New observation of this work is that the dark charge is broken down to two kinds of dark parity, $Z_2$ and $Z'_2$, which subsequently imply three scenarios of dark matter. The relic density and direct detection for the scenario of two-component dark matter are investigated in detail.

Constraints for electric charge from Maxwell’s equations and boundary conditions

Certain boundary conditions constrain the forms that the electromagnetic field can take in a theory, in particular the boundary conditions inherent to closed spaces. According to Maxwell’s equations, this can give rise to constraints for the electric charge in the theory. We identify three such ‘boundary constraints’ for electric charge and highlight some of their myriad implications, touching upon a wealth of topics including the self-consistency of practical calculations, the nature of dark matter, the origin of electric-charge quantisation and the shape of the Universe. Furthermore, we explain that magnetic analogues of our boundary constraints offer new insights into the possible existence of magnetic monopoles and dyons.

$SU(5)_{L} \times U(1)_{Y}$ electroweak unification

Abstract We propose here—for the first time in the literature, to our best knowledge—an electroweak unification based on the $SU(5)_{L}\times U(1)_{Y}$ gauge group. The spontaneous symmetry breaking takes place in the manner $SU(5)_{L}\times U(1)_{Y} \rightarrow U(1)_{em}$, due to a particular Higgs sector consisting of five scalar quintuplets. Each scalar quintuplet acquires its own vacuum expectation value, by means of a proper parametrization which is worked out once an overall vacuum expectation value in the model is established. The decoupling of the low-energy regime (corresponding to the Standard Model) from the high scale (required by our model here) is straightforwardly achieved in order to preserve the consistency with the present experimental data. Finally, a promising phenomenological outcome is derived by simply tuning a single free parameter. Our results also include, besides a viable one-parameter mass spectrum, the prediction of precisely three generations in the fermion sector and the electric charge quantization.

Acceleration in quantum mechanics and electric charge quantization

In this study, we have discussed the implications of acceleration in quantum mechanics by means of a generalized derivative operator (GDO). A new Schrödinger equation is obtained which depends on the reduced Compton wavelength of the particle. We have discussed its implications in quantum mechanics for different types of potentials mainly the infinite wall potential, the gravitational linear field potential, the Cornell potential and the Coulomb repulsive potential. The corresponding wave functions and discrete energies are modified and differ from the results obtained in the conventional formalism. The major results obtained concerned the large improvement of the ground energy of the electron subject to the gravitational acceleration in addition to Cornell potential and the emergence of quantized electric charge in the theory without including Dirac monopoles or using gauge theories.

Electric charge quantization in SU(3)c ⊗ SU(n)L ⊗ U(1)Y gauge models

We prove that the Cotăescu general method of solving SU(3)c ⊗ SU(n)L ⊗ U(1)Y gauge models exactly predicts the observed electric charge quantization, as the theory remains renormalizable, both in its strong and electroweak sectors, while all the fermions get their masses—by means of Yukawa terms—the spontaneous symmetry breakdown (SSB) successively. The latter is achieved by a scalar sector consisting of n Higgs multiplets, each acquiring its own vacuum expectation value (VEV).

A CMB Millikan experiment with cosmic axiverse strings

We study axion strings of hyperlight axions coupled to photons. Hyperlight axions — axions lighter than Hubble at recombination — are a generic prediction of the string axiverse. These axions strings produce a distinct quantized polarization rotation of CMB photons which is mathcal{O} (αem). As the CMB light passes many strings, this polarization rotation converts E-modes to B-modes and adds up like a random walk. Using numerical simulations we show that the expected size of the final result is well within the reach of current and future CMB experiments through the measurement of correlations of CMB B-modes with E- and T-modes. The quantized polarization rotation angle is topological in nature and can be seen as a geometric phase. Its value depends only on the anomaly coefficient and is independent of other details such as the axion decay constant. Measurement of the anomaly coefficient by measuring this rotation will provide information about the UV theory, such as the quantization of electric charge and the value of the fundamental unit of charge. The presence of axion strings in the universe relies only on a phase transition in the early universe after inflation, after which the string network rapidly approaches an attractor scaling solution. If there are additional stable topological objects such as domain walls, axions as heavy as 10−15 eV would be accessible. The existence of these strings could also be probed by measuring the relative polarization rotation angle between different images in gravitationally lensed quasar systems.

Electric charge quantisation in 331 models with exotic charges

The extensions of the Standard Model based on the $SU(3)_{C} \otimes SU(3)_{L} \otimes U(1)_{X}$ gauge group are known as 331 Models. Different properties such as the fermion assignment and the electric charges of the exotic spectrum, that defines a particular 331 model, are fixed by a $\beta$ parameter. In this article we study the electric charge quantization in two versions of the 331 models, set by the conditions $\beta=1/\left( 3\sqrt{3}\right)$ and $\beta=0$. In these frameworks, arise exotic particles, for instance, new leptons and gauge bosons with a fractional electric charge. Additionally, depending on the version, quarks with non-standard fractional electric charges or even neutral appear. Considering the definition of electric charge operator as a linear combination of the group generators that annihilates the vacuum, classical constraints from the invariance of the lagrangian, and gauge and mixed gauge-gravitational anomalies cancellation, the quantization of the electric charge can be verified in both versions.

On a geometric origin of the electric charge quantization

The field-line description of the electric field, proposed by Faraday, accepted by Maxwell and used by Dirac, is utilized here in order to try to understand the origin of the electric charge quantization. This origin could be the result of the discrete nature of the field lines in conjunction with the requirement for spherical symmetry of the field. Under the hypothesis that for elementary particles, the electric field is consisting of only a few field lines, the d-quark could be composed of four field lines, the u-quark of eight, and the electron of 12. The proton would also exhibit a 12 field line structure. For electrons and protons, such a structure could eventually be observed with the here proposed experimental techniques. New particles with charges 1/2e, 5/3e, and 2.5e would be allowed in this context.

Finite and half-infinite solenoids and the Aharonov-Bohm effect

In quantum mechanics, the magnetic field has a physical effect beyond its local presence. For axially symmetric vector potentials, A=A(s,z)ϕ̂, it is the magnetic flux that plays a central role in both interference experiments (as in the Aharonov-Bohm effect) and in bound state spectra for a particle constrained to move in a circle. The flux dependence is evident in various configurations, and we have chosen two applications to highlight the non-local nature of the quantum mechanical magnetic field dependence: A finite solenoid and a Dirac string with a non-zero radius. The finite solenoid is interesting because it represents the actual experimental apparatus for measuring the Aharonov-Bohm effect. The Dirac string provides an electric charge quantization mechanism that depends on where the quantization argument is applied, yielding different fundamental charge units for different locations.

Geometrical unification of gravitation and electromagnetism

A theory which achieves a complete geometrical unification of gravitation and electromagnetism (GUGE) is presented. This new theory is based on a recent proposal of proper time redefinition that leads to the construction of a Riemann metric, which naturally unifies gravity and electromagnetism. The 5--dimensional Riemann metric which arises looks exactly the same as the one postulated in the Kaluza-Klein (KK) 5-dimensional theory. Nevertheless, there are deep differences between GUGE and KK. The GUGE metric is deduced while the KK metric is postulated. In the GUGE field theory there is no need to impose either of the so called "cylinder" or "curling of coordinates" conditions, because they emerge as direct consequences of the construction of the GUGE metric. The GUGE field equations are fully equivalent to Einstein--Maxwell equations, while KK field equations are not. The GUGE 5--dimensional (geodesic) equations are equivalent to the 4--dimensional (non--geodesic) equations for a charged particle moving in the presence of gravitational and electromagnetic fields, unlike the KK 5--dimensional (geodesic) equations which are not and, in addition, yield non--gauge covariant geodesic equations. No extra scalar field appears in GUGE. The physical interpretation of the fifth dimension and of the role of the extra field in KK (internal coordinate in GUGE) are totally different in both approaches. Finally, GUGE results include electric charge conservation, electric charge quantization and electric charge contribution to the energy of charged particles even in the absence of electromagnetic fields, which implies (the observed fact) that there are no massless electrically charged particles in Nature, unlike the prevailing treatments of KK theories.

The Entropic Dynamics Approach to Quantum Mechanics

Entropic Dynamics (ED) is a framework in which Quantum Mechanics is derived as an application of entropic methods of inference. In ED the dynamics of the probability distribution is driven by entropy subject to constraints that are codified into a quantity later identified as the phase of the wave function. The central challenge is to specify how those constraints are themselves updated. In this paper we review and extend the ED framework in several directions. A new version of ED is introduced in which particles follow smooth differentiable Brownian trajectories (as opposed to non-differentiable Brownian paths). To construct ED we make use of the fact that the space of probabilities and phases has a natural symplectic structure (i.e., it is a phase space with Hamiltonian flows and Poisson brackets). Then, using an argument based on information geometry, a metric structure is introduced. It is shown that the ED that preserves the symplectic and metric structures—which is a Hamilton-Killing flow in phase space—is the linear Schrödinger equation. These developments allow us to discuss why wave functions are complex and the connections between the superposition principle, the single-valuedness of wave functions, and the quantization of electric charges. Finally, it is observed that Hilbert spaces are not necessary ingredients in this construction. They are a clever but merely optional trick that turns out to be convenient for practical calculations.

All roads lead to the Dirac quantization condition

The existence of magnetic monopoles is a sufficient argument to explain the quantization of electric charge, an argument that was presented by Dirac. Regardless of the status of any search for magnetic monopoles, the formal description of the quantum mechanics of a charged particle in the field of a magnetic monopole is very rich and has increased our understanding of the mathematical structures underlying this description, as well as of its physical implications. In this short review, we present four different arguments all leading to the Dirac quantization condition, emphasizing their geometrical and topological aspects.

Charged gravitational instantons: extra CP violation and charge quantisation in the Standard Model

We argue that quantum electrodynamics combined with quantum gravity results in a new source of CP violation, anomalous non-conservation of chiral charge and quantisation of electric charge. Further phenomenological and cosmological implications of this observation are briefly discussed within the standard model of particle physics and cosmology.

Electromagnetic duality and central charge

We provide a full realization of the electromagnetic duality at the boundary by extending the phase space of Maxwell's theory through the introduction of edge modes and their conjugate momenta. We show how such extension, which follows from a boundary action, is necessary in order to have well defined canonical generators of the boundary magnetic symmetries. In this way, both electric and magnetic soft modes are encoded in a boundary gauge field and its conjugate dual. This implementation of the electromagnetic duality has striking consequences. In particular, we show first how the electric charge quantization follows straightforwardly from the topological properties of the $U(1)$-bundle of the boundary dual potential. Moreover, having a well defined canonical action of the electric and magnetic symmetry generators on the phase space, we can compute their algebra and reveal the presence of a central charge between them. We conclude with possible implications of these results in the quantum theory.