Quantization Of Electric Charge Research Articles

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.

Dirac quantisation condition: a comprehensive review

ABSTRACTIn most introductory courses on electrodynamics, one is taught the electric charge is quantised but no theoretical explanation related to this law of nature is offered. Such an explanation is postponed to graduate courses on electrodynamics, quantum mechanics and quantum field theory, where the famous Dirac quantisation condition is introduced, which states that a single magnetic monopole in the Universe would explain the electric charge quantisation. Even when this condition assumes the existence of a not-yet-detected magnetic monopole, it provides the most accepted explanation for the observed quantisation of the electric charge. However, the usual derivation of the Dirac quantisation condition involves the subtle concept of an ‘unobservable’ semi-infinite magnetised line, the so-called ‘Dirac string,’ which may be difficult to grasp in a first view of the subject. The purpose of this review is to survey the concepts underlying the Dirac quantisation condition, in a way that may be accessible to advanced undergraduate and graduate students. Some of the discussed concepts are gauge invariance, singular potentials, single-valuedness of the wave function, undetectability of the Dirac string and quantisation of the electromagnetic angular momentum. Five quantum-mechanical and three semi-classical derivations of the Dirac quantisation condition are reviewed. In addition, a simple derivation of this condition involving heuristic and formal arguments is presented.

Spin-1 topological monopoles in the parameter space of ultracold atoms

Magnetic monopole, a hypothetical elementary particle with isolated magnetic pole, is crucial for the quantization of electric charge. In recent years, analogues of magnetic monopoles, represented by topological defects in parameter spaces, have been studied in a wide range of physical systems. These works mainly focused on Abelian Dirac monopoles in spin-1/2 or non-Abelian Yang monopoles in spin-3/2 systems. Here we propose to realize three types of spin-1 topological monopoles and study their geometric properties using the parameter space formed by three hyperfine states of ultracold atoms coupled by radio-frequency fields. These spin-1 monopoles, characterized by different monopole charges, possess distinct Berry curvature fields and spin textures, which are directly measurable in experiments. The topological phase transitions between different monopoles are accompanied by the emergence of spin "vortex", and can be intuitively visualized using Majorana's stellar representation. We show how to determine the Berry curvature, hence the geometric phase and monopole charge from dynamical effects. Our scheme provides a simple and highly tunable platform for observing and manipulating spin-1 topological monopoles, paving the way for exploring new topological quantum matter.

Index theorem for non-supersymmetric fermions coupled to a non-Abelian string and electric charge quantization

Non-Abelian strings are considered in non-supersymmetric theories with fermions in various appropriate representations of the gauge group U[Formula: see text]. We derive the electric charge quantization conditions and the index theorems counting fermion zero modes in the string background both for the left-handed and right-handed fermions. In both cases we observe a non-trivial [Formula: see text] dependence.

Search for an electric charge of the neutron

The electrical neutrality of the neutron is linked to the electric charge quantization. It is not understood yet if the electric charge is quantized or not. Since the discovery of the neutron, many attempts have been made to measure its electric charge ${q}_{n}$ directly and indirectly. We present a method to search for a possible ${q}_{n}$ by means of an optical setup using ultracold neutrons. In a first run, a statistical sensitivity of $\ensuremath{\delta}{q}_{n}=2.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20}\text{ }\text{ }e/\sqrt{\mathrm{day}}$ is achieved. Possible improvements to increase this sensitivity down to $\ensuremath{\delta}{q}_{n}\ensuremath{\approx}1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}21}\text{ }\text{ }e/\sqrt{\mathrm{day}}$ are found and discussed.

Search for magnetic monopoles with the MoEDAL forward trapping detector in 13 TeV proton-proton collisions at the LHC

The MoEDAL experiment addresses a decades-old issue, the search for an elementary magnetic monopole, first theorised in 1931 by Dirac to explain electric charge quantisation. Since then it was showed that magnetic monopoles occur naturally in grand unified theories as solutions of classical equations of motion. The dedicated experiment can enjoy a new energy regime opened at the LHC allowing direct probes of magnetic monopoles at the TeV scale for the first time. MoEDAL pioneered a technique in which monopoles would be slowed down in a dedicated aluminium array and the presence of trapped monopoles is probed by analysing the samples with a superconducting magnetometer. The MoEDAL forward trapping detector array deployed in 2015 was analysed and found consistent with zero trapped magnetic charge, allowing to set the first LHC constraints for monopoles carrying twice or thrice the Dirac charge.

Magnetic monopoles and free fractionally charged states at accelerators and in cosmic rays

Unified theories of strong, weak and electromagnetic interactions which have electric charge quantization predict the existence of topologically stable magnetic monopoles. Intermediate scale monopoles are comparable with detection energies of cosmic ray monopoles at IceCube and other cosmic ray experiments. Magnetic monopoles in some models can be significantly lighter and carry two, three or possibly even higher quanta of the Dirac magnetic charge. They could be light enough for their effects to be detected at the LHC either directly or indirectly. An example based on a D-brane inspired SU(3)C × SU(3)L × SU(3)R (trinification) model with the monopole carrying three quanta of Dirac magnetic charge is presented. These theories also predict the existence of color singlet states with fractional electric charge which may be accessible at the LHC.

An RRAM-based MLC design approach

RRAM is an emerging technology with vast applications in computation and storage. RRAM with MLC capabilities is more interesting owing to its higher storage density. In this study, we proposed an approach for RRAM-based MLC design. The approach starts with capacitor-based quantization of electric charge applying to RRAM. Numerical characterizations of a unit-circuit, including RRAM, capacitor and one MOS transistor were used. Two Stanford and Peking-Stanford RRAM models were employed in this study. The proposed design results in simplified circuitry and avoids power hungry elements (e.g. Op-Amp). A detailed RRAM-based MLC memory array is implemented. To simplify the memory read process, a TIQ-ADC is employed. To evaluate the approach, circuit-level mixed SPICE/Verilog-A simulations were performed. The variation and random effects are experimented using Monte-Carlo simulations. The costs of the proposed approach are design-time pre-computation and complexity of one-time device characterization.

Advantages of unity with SU(4)-color: Reflections through neutrino oscillations, baryogenesis and proton decay

Advantages of unity with SU(4)-color: Reflections through neutrino oscillations, baryogenesis and proton decay

Non-Abelian monopoles as the origin of dark matter

We suggest that dark matter may be partially constituted by a dilute ’t Hooft–Polyakov monopoles gas. We reach this conclusion by using the Georgi–Glashow model coupled to a dual kinetic mixing term [Formula: see text] where [Formula: see text] is the electromagnetic field and [Formula: see text] the ’t Hooft tensor. We show that these monopoles carry both (Maxwell) electric and (Georgi–Glashow) magnetic charges and the electric charge quantization condition is modified in terms of a dimensionless real parameter. This parameter could be determined from milli-charged particle experiments.

Electric charge quantization in [formula omitted] models

We show how in a model based on the gauge group SU(3)c⊗SU(4)L⊗U(1)X, the quantization of the electric charge can be explained.

Unifying the electroweak andB−Linteractions

We argue that the gauge symmetry which includes SU(3)_L as a higher weak-isospin symmetry is manifestly given by SU(3)_C\otimes SU(3)_L\otimes U(1)_X\otimes U(1)_N, where the last two factors determine the electric charge and B-L, respectively. This theory not only provides a consistent unification of the electroweak and B-L interactions, but also gives insights in dark matter, neutrino masses, and inflation. The dark matter belongs to a class of new particles that have wrong B-L numbers, and is stabilized due to a newly-realized W-parity as residual gauge symmetry. The B-L breaking field is important to define the W-parity, seesaw scales, and inflaton. Furthermore, the number of fermion generations and the electric charge quantization are explained naturally. We also show that the previous 3-3-1 models are only an effective theory as the B-L charge and the unitarity argument are violated. This work substantially generalizes our recently-proposed 3-3-1-1 model.

Electric charge quantization in SU(3)c ⊗SU(4)L ⊗U(1)X models

We obtain electric charge quantization in the context of models based on the gauge symmetry group SU (3)c ⊗ U (4)L ⊗U(1)X. The gauge models study include three families to cancel out anomalies and a set of scalar fields to break the symmetry spontaneously. To show the electric charge quantization, we use classical symmetry conditions and quantum chiral anomaly conditions.

Observation of Dirac monopoles in a synthetic magnetic field

Magnetic monopoles--particles that behave as isolated north or south magnetic poles--have been the subject of speculation since the first detailed observations of magnetism several hundred years ago. Numerous theoretical investigations and hitherto unsuccessful experimental searches have followed Dirac's 1931 development of a theory of monopoles consistent with both quantum mechanics and the gauge invariance of the electromagnetic field. The existence of even a single Dirac magnetic monopole would have far-reaching physical consequences, most famously explaining the quantization of electric charge. Although analogues of magnetic monopoles have been found in exotic spin ices and other systems, there has been no direct experimental observation of Dirac monopoles within a medium described by a quantum field, such as superfluid helium-3 (refs 10-13). Here we demonstrate the controlled creation of Dirac monopoles in the synthetic magnetic field produced by a spinor Bose-Einstein condensate. Monopoles are identified, in both experiments and matching numerical simulations, at the termini of vortex lines within the condensate. By directly imaging such a vortex line, the presence of a monopole may be discerned from the experimental data alone. These real-space images provide conclusive and long-awaited experimental evidence of the existence of Dirac monopoles. Our result provides an unprecedented opportunity to observe and manipulate these quantum mechanical entities in a controlled environment.

Quantization of area for event and Cauchy horizons of the Kerr-Newman black hole

Based on various string theoretic constructions, and various string-inspired generalizations thereof, there have been repeated suggestions that the areas of black hole event horizons might be quantized in a quite specific manner, in terms of linear combinations of square roots of positive integers. It is important to realise that there are significant physical constraints on such integer-based proposals when one (somewhat speculatively) attempts to extend them outside their original extremal and supersymmetric framework. Specifically, in their most natural and direct physical interpretations, some of the more speculative integer-based proposals for the quantization of horizon areas fail for the ordinary Kerr-Newman black holes in (3+1) dimensions, essentially because the fine structure constant is not an integer. A more baroque interpretation involves asserting the fine structure constant is the square root of a rational number; but such a proposal has its own problems. Insofar as one takes (3+1) general relativity (plus the usual quantization of angular momentum and electric charge) as being paramount, the known explicitly calculable spectra of horizon areas for the physically compelling Kerr-Newman spacetimes indicate that some caution is called for when assessing the universality of some of the more speculative integer-based string-inspired proposals.

An Alternative Approach to the Electric Charge Quantization with Non-global Potentials

We present an alternative approach to justify the electric charge quantization by means of non-global electromagnetic potentials. We adopt a non-global potential whose singularity does not goes over to infinity and can be entirely embedded into an arbitrarily small closed ball.

Electric-charge quantization in gauge theories

The electric-charge quantization and fixing conditions of particles are found using a number of gauge theories, and it is shown that the presence of Higgs fields is a necessary condition for the electric-charge quantization in the considered models.

Principal bundles and topological quantization of charges

The space of admissible particle velocities is assumed to be a four-dimensional nonholonomic distribution on a principal or associated bundle. Equations for the horizontal geodesics of this distribution coincide with the equations of motion of charged particles in general relativity theory. It is proved that, if the Lie group of the standard model of elementary particle physics is augmented by the 4-torus, then the wave functions are eigenfunctions of charge operators and the horizontal lift does not depend on the coupling constants. These wave functions satisfy the well-known Dirac equation and its generalizations. For such wave functions, the topological quantization of electric, lepton, and baryon charges takes place.

Millikan Movies

Since Robert Millikan discovered the quantization of electric charge and measured its fundamental value over 90 years ago, his oil-drop experiment has become essential in physics laboratory classes at both the high school and college level. As physics instructors, however, many of us have used the traditional setup and experienced the tedium of collecting data and the frustration of students who obtain disappointing results for the charges on individual oil drops after two or three hours of hard work. Some novel approaches have been developed to make the data collection easier and more accurate. One method is to attach a CCD (charge coupled device) camera to the microscope of the traditional setup.1,2 Through the CCD camera, the motion of an oil drop can be displayed on a TV monitor1 and/or on a computer.2 This allows several students to view the image of a droplet simultaneously instead of taking turns squinting through the tiny microscope eyepiece on the traditional setup. Furthermore, the motion of an oil drop can be captured and analyzed using software such as VideoPoint,3 which enhances the accuracy of the measurement of the charge on each oil drop.2 While these innovative methods improve the convenience and efficiency with which data can be collected, an instructor has to invest a considerable amount of money and time so as to adapt the new techniques to his or her own classroom. In this paper, we will report on the QuickTime movies we made, which can be used to analyze the motions of 16 selected oil drops. These digital videos are available on the web4 for teachers to download and use with their own students. We will also share the procedure for analyzing the videos using Logger Pro,5 as well as our results for the charges on the oil drops and some pedagogical aspects of using the movies with students.

Generalized gauge transformations in phase space picture of quantum mechanics: Kirkwood representation

Here, the ordinary gauge transformations in configuration space are generalized to the phase space. The corresponding gauge functions are separable in terms of those of the configuration and the momentum spaces. Furthermore, we consider the gauge transformations in phase space for which their gauge functions are not, in general, separable. It is shown that, the assumption of the general global gauge symmetry in phase space immediately yields the quantization of the electric charge. We obtain this result without assuming the concept of the magnetic monopole that Dirac did in his approach to the problem of electric charge quantization and which is not detected yet.