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1

Georgescu, Iulia. "Charge conservation." Nature Physics 11, no. 12 (December 2015): 987. http://dx.doi.org/10.1038/nphys3599.

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2

Doria, R. M., and I. Soares. "Four Bosons EM Conservation Laws." JOURNAL OF ADVANCES IN PHYSICS 19 (May 27, 2021): 40–92. http://dx.doi.org/10.24297/jap.v19i.9024.

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Electromagnetism is expressed from two basic postulates. They are light invarianceand charge conservation. At this work one extends the Maxwell scenario from macroscopic to microscopic electromagnetism by following the elementary particles electric charge microscopic behavior. It yields a triune electric charge interrelationship. Three charges {+, 0, −} be exchanged through a vector bosons quadruplet. It is called Four Bosons Electromagnetism. A systemic EM physics appears to be understood. Maxwell photon is not enough for describing the microscopic electric charge physics. An extension for electromagnetic energy is obtained. The fields quadruplet {Aµ, Uµ, Vµ±} are the porters of electromagnetic energy. They are the usual photon Aµ, massive photon Uµ and two charged photons Vµ±, A new understanding on EM phenomena has to be considered. A set determinism based on granular and collective fields is developed. A space-time evolution associated to a whole.Conservation laws are studied. The EM phenomena is enlarged to three charges interchanges to {+, 0, −}. Two novelties appear. New features on nonlinear fields acting as own sources and on electric charge physics. Properties as conservation, conduction, transmission, interaction are extended to a systemic electromagnetism. A whole conservation law for electric charge emerges from three charges interwoven. Electric charge has a systemic behavior. Although there is no Coulomb law for zero electric charge, the Four Bosons Electromagnetism contains an EM energy which provides a neutral electromagnetism. Particles with zero charge {Aµ, Uµ} are carrying EM energy. Another consideration is on EM energy being transported by four nonlinear fields. A new physicality appears. The abelian nonlinearity generates fields charges. Fields are working as own sources through mass terms, trilinear and quadrilinear interactions, spin couplings. Consequently the photon is more than being a consequence from electric charge oscillations. It is able to generate its own charge. Introduce the meaning of photonics.Thus, electric charge is no more the isolate electromagnetic source. There are another conservation laws. Fields sources appear through corresponding equations of motion, Bianchi identities, energy-momentum, Noether laws and angular momentum conservation laws. They move EM to a fields charges dependence. Together with electric charge they carrythe electromagnetic flux. Supporting the Ahranov-Bohm experiment of potential fields as primitive entities.
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3

Rueckner, Wolfgang, Douglass Goodale, Daniel Rosenberg, and David Tavilla. "Demonstration of charge conservation." American Journal of Physics 63, no. 1 (January 1995): 90–91. http://dx.doi.org/10.1119/1.17778.

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4

Chaichian, M., J. A. Gonzales, C. Montonen, and H. Perez Rojas. "Classical charge non-conservation." Physics Letters B 300, no. 1-2 (February 1993): 118–20. http://dx.doi.org/10.1016/0370-2693(93)90757-9.

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5

Silver, G. L. "Charge balance vs. charge conservation for plutonium." Journal of Radioanalytical and Nuclear Chemistry Letters 154, no. 2 (May 1991): 133–37. http://dx.doi.org/10.1007/bf02162671.

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6

Doria, Renato, J. Chauca, and I. Soares. "Four Bosons Electromagnetism." JOURNAL OF ADVANCES IN PHYSICS 10, no. 1 (August 5, 2015): 2610–40. http://dx.doi.org/10.24297/jap.v10i1.1341.

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Based on light invariance and electric conservation a four bosons electromagnetism is proposed. It enlarges the electric charge conservation beyond displacement current and Dirac charge to a new physical situation where the electromagnetic phenomena is mediated by the usual photon plus a massive photon and two additional charged vector bosons.Considering the enlarged abelian gauge symmetry U(1) SO(2) transforming under a same gauge parameter a non-linear electromagnetism involving four bosons is introduced. It deploys a Lagrangian containing massless, massive and charged elds with three and four vector bosons interactions. The corresponding Noether's relations and classical equations of motion are studied. They provide a whole dynamics involving granular, collective terms through antisymmetric and symmetric sectors. It develops a new photon equation which extends the Maxwell's one. Self interacting photons are obtained.A four boson electromagnetic ux is derived. It expresses an electromagnetism transfering 4Q = 0 and j4Qj = 1, not more limited to just a massless photon. There is a new electromagnetic owing to be understood, where aside of electric charge conservation, it appears a neutral electromagnetism. There are six neutral electromagnetic charges beyond electric charge as consequences from non-linearity. Two are derived from the second Noether identity and four from variational continuity equations. An electromagnetic ux being conducted by a whole physics is generated. Based on elds set, it develops a determinism under the meaning of directive and circumstance. Interpreting that, light invariance concises the photon as directive, the photon becomes a whole maker. It assumes the symmetry command which will control the conservations laws and opportunities. Consequently, one combines the symmetry equation derived fromNoether theorem with the four equations derived from variational principle, and an effective photon equation is obtained. A kind of Navier-Stokes electromagnetic ow is derived. It yields a four bosons electromagnetism preserving electric charge conservation plus introducting the meaning of chance through symmetry management.
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7

Huggins, Elisha, and Drew Milsom. "Lorentz Transformation and Charge Conservation." Physics Teacher 45, no. 6 (September 2007): 328–29. http://dx.doi.org/10.1119/1.2768683.

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8

Looser, Herbert. "Lorentz Transformation and Charge Conservation." Physics Teacher 46, no. 1 (January 2008): 4–5. http://dx.doi.org/10.1119/1.2823988.

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9

Ord, G. N. "Quantum interference from charge conservation." Physics Letters A 173, no. 4-5 (February 1993): 343–46. http://dx.doi.org/10.1016/0375-9601(93)90247-w.

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10

MATUTE, ERNESTO A. "A TOPOLOGICAL VIEW ON BARYON NUMBER CONSERVATION." Modern Physics Letters A 19, no. 19 (June 21, 2004): 1469–82. http://dx.doi.org/10.1142/s0217732304013738.

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We argue that the charge fractionalization in quarks has a hidden topological character related to a broken [Formula: see text] symmetry between integer-charged bare quarks and leptons. The mechanism is a tunneling process occurring in time between standard field configurations of a pure gauge form with different topological winding numbers associated with integer-charged bare quarks in the far past and future. This transition, which nonperturbatively normalizes local bare charges with a universal accumulated value, corresponds to a specific topologically nontrivial configuration of the weak gauge fields in Euclidean spacetime. The outcome is an effective topological charge equal to the ratio between baryon number and the number of fermion generations associated with baryonic matter. The observed conservation of baryon number is then related to the conservation of this bookkeeping charge on quarks. Baryon number violation may only arise through topological effects as in decays induced by electroweak instantons. However, stability of a free proton is expected.
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11

Horikawa, Yataro, and Yasutoshi Tanaka. "Charge conservation for nonrelativistic RPA theory." Physics Letters B 409, no. 1-4 (September 1997): 1–5. http://dx.doi.org/10.1016/s0370-2693(97)00903-9.

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12

Arnoldus, Henk F. "Conservation of charge at an interface." Optics Communications 265, no. 1 (September 2006): 52–59. http://dx.doi.org/10.1016/j.optcom.2006.03.024.

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13

Ko, C. M., V. Koch, Zi-wei Lin, K. Redlich, M. Stephanov, and Xin-Nian Wang. "Kinetic Equation with Exact Charge Conservation." Physical Review Letters 86, no. 24 (June 11, 2001): 5438–41. http://dx.doi.org/10.1103/physrevlett.86.5438.

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14

Rueckner, Wolfgang. "An improved demonstration of charge conservation." American Journal of Physics 75, no. 9 (September 2007): 861–63. http://dx.doi.org/10.1119/1.2721589.

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15

HORIKAWA, YATARO. "Charge conservation for Landau-Migdal theory." Juntendo Medical Journal 42, Supplement (1997): S18—S26. http://dx.doi.org/10.14789/pjmj.42.s18.

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16

Bao-an, Yao, Zhang Chun-sheng, and Lin Qing. "Charge conservation and CCD aperture photometry." Chinese Astronomy and Astrophysics 30, no. 3 (July 2006): 342–50. http://dx.doi.org/10.1016/j.chinastron.2006.07.013.

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17

JINGHUA, FU. "NET CHARGE FLUCTUATION AS A MEASURE OF LOCAL CHARGE CONSERVATION." International Journal of Modern Physics E 16, no. 10 (November 2007): 3339–46. http://dx.doi.org/10.1142/s0218301307009312.

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It is demonstrated in this paper that, in terms of a schematic multiperipheral model, net charge fluctuation satisfies the same Quigg–Thomas relation as satisfied by charge transfer fluctuation. Net charge fluctuations measured in finite rapidity windows depend on both the local charge correlation length and the size of the observation window. When the observation window is larger than the local charge correlation length, the net charge fluctuation only depends on the local charge correlation length and can be used as a measure of local charge correlation length.
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18

Gratus, Jonathan, Paul Kinsler, and Martin W. McCall. "Charge Conservation: Temporary Singularities and Axions: An Analytic Solution that Challenges Charge Conservation (Ann. Phys. 6/2021)." Annalen der Physik 533, no. 6 (June 2021): 2170021. http://dx.doi.org/10.1002/andp.202170021.

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19

TSAN, UNG CHAN. "MASS, MATTER, MATERIALIZATION, MATTERGENESIS AND CONSERVATION OF CHARGE." International Journal of Modern Physics E 22, no. 05 (May 2013): 1350027. http://dx.doi.org/10.1142/s0218301313500274.

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Conservation of mass in classical physics and in chemistry is considered to be equivalent to conservation of matter and is a necessary condition together with other universal conservation laws to account for observed experiments. Indeed matter conservation is associated to conservation of building blocks (molecules, atoms, nucleons, quarks and leptons). Matter is massive but mass and matter are two distinct concepts even if conservation of mass and conservation of matter represent the same reality in classical physics and chemistry. Conservation of mass is a consequence of conservation of atoms. Conservation of mass is valid because in these cases it is a very good approximation, the variation of mass being tiny and undetectable by weighing. However, nuclear physics and particle physics clearly show that conservation of mass is not valid to express conservation of matter. Mass is one form of energy, is a positive quantity and plays a fundamental role in dynamics allowing particles to be accelerated. Origin of mass may be linked to recently discovered Higgs bosons. Matter conservation means conservation of baryonic number A and leptonic number L, A and L being algebraic numbers. Positive A and L are associated to matter particles, negative A and L are associated to antimatter particles. All known interactions do conserve matter thus could not generate, from pure energy, a number of matter particles different from that of number of antimatter particles. But our universe is material and neutral, this double message has to be deciphered simultaneously. Asymmetry of our universe demands an interaction which violates matter conservation but obeys all universal conservation laws, in particular conservation of electric charge Q. Expression of Q shows that conservation of (A–L) and total flavor TF are necessary and sufficient to conserve Q. Conservation of A and L is indeed a trivial case of conservation of (A–L) and is valid for all known interactions of the standard model. Assumption of a novel interaction MC conserving (A–L) but violating simultaneously A and L (not trivial case of conservation) would allow energy to be transformed into a pair of baryon lepton or into a pair of antibaryon antilepton of opposite charges. This model could explain the asymmetric but nevertheless electrically neutral Universe but could not account for the numerical value of the tiny excess of matter over antimatter. The concept of anti-Universe would be superfluous. Observation of matter nonconservation processes would be of great interest to falsify this speculation.
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20

Begun, V. "Charge Conservation Effects for High-order Fluctuations." Acta Physica Polonica B Proceedings Supplement 10, no. 3 (2017): 901. http://dx.doi.org/10.5506/aphyspolbsupp.10.901.

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21

Arminjon, Mayeul. "On Charge Conservation in a Gravitational Field." Geometry, Integrability and Quantization 19 (2018): 57–65. http://dx.doi.org/10.7546/giq-19-2018-57-65.

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22

Roux, Filippus S. "Polynomial Gaussian beams and topological charge conservation." Optics Communications 266, no. 2 (October 2006): 433–37. http://dx.doi.org/10.1016/j.optcom.2006.05.038.

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23

Novikov, V. A. "CPT breaking and electric charge non-conservation." Journal of Physics: Conference Series 675, no. 1 (February 5, 2016): 012007. http://dx.doi.org/10.1088/1742-6596/675/1/012007.

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24

Zapolsky, Harold S. "Does charge conservation imply the displacement current?" American Journal of Physics 55, no. 12 (December 1987): 1140. http://dx.doi.org/10.1119/1.15263.

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25

Roux, Filippus S. "Topological charge conservation in stochastic optical fields." Journal of Optics 18, no. 5 (March 14, 2016): 054005. http://dx.doi.org/10.1088/2040-8978/18/5/054005.

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26

Modanese, G. "Generalized Maxwell equations and charge conservation censorship." Modern Physics Letters B 31, no. 06 (February 28, 2017): 1750052. http://dx.doi.org/10.1142/s021798491750052x.

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The Aharonov–Bohm electrodynamics is a generalization of Maxwell theory with reduced gauge invariance. It allows to couple the electromagnetic field to a charge which is not locally conserved, and has an additional degree of freedom, the scalar field [Formula: see text], usually interpreted as a longitudinal wave component. By reformulating the theory in a compact Lagrangian formalism, we are able to eliminate S explicitly from the dynamics and we obtain generalized Maxwell equation with interesting properties: they give [Formula: see text] as the (conserved) sum of the (possibly non-conserved) physical current density [Formula: see text], and a “secondary” current density [Formula: see text] which is a nonlocal function of [Formula: see text]. This implies that any non-conservation of [Formula: see text] is effectively “censored” by the observable field [Formula: see text], and yet it may have real physical consequences. We give examples of stationary solutions which display these properties. Possible applications are to systems where local charge conservation is violated due to anomalies of the Adler–Bell–Jackiw (ABJ) kind or to macroscopic quantum tunnelling with currents which do not satisfy a local continuity equation.
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27

Shih, Chia C., and P. Carruthers. "Stochastical dynamics and charge conservation in hadronization." Physical Review D 38, no. 1 (July 1, 1988): 56–63. http://dx.doi.org/10.1103/physrevd.38.56.

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28

Manno, Gianni, Juha Pohjanpelto, and Raffaele Vitolo. "Gauge invariance, charge conservation, and variational principles." Journal of Geometry and Physics 58, no. 8 (August 2008): 996–1006. http://dx.doi.org/10.1016/j.geomphys.2008.03.006.

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29

Gibiino, Gian Piero, Alberto Santarelli, and Fabio Filicori. "Charge-conservative GaN HEMT nonlinear modeling from non-isodynamic multi-bias S-parameter measurements." International Journal of Microwave and Wireless Technologies 11, no. 5-6 (February 8, 2019): 431–40. http://dx.doi.org/10.1017/s1759078719000059.

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AbstractGuaranteeing charge conservation of empirically extracted Gallium Nitride (GaN) High-Electron-Mobility Transistor (HEMT) models is necessary to avoid simulation issues and artifacts in the prediction. However, dispersive effects, such as thermal and charge-trapping phenomena, may compromise the model extraction flow resulting in poor model accuracy. Although GaN HEMT models should be extracted, in principle, from an isodynamic dataset, this work deals with the systematic identification of an approximate, yet most suitable, charge-conservative empirical model from standard multi-bias S-parameters, i.e., from non-isodynamic data. Results show that the obtained model maintains a reasonable accuracy in predicting both small- and large-signal behavior, while providing the benefits of charge conservation.
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30

Horák, Michal. "Conservation laws and charge transport across heterojunction barriers." Solid-State Electronics 42, no. 2 (March 1998): 269–76. http://dx.doi.org/10.1016/s0038-1101(97)00222-0.

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31

Ng, Chung-Sang. "Energy conservation of a uniformly accelerated point charge." Physical Review E 47, no. 3 (March 1, 1993): 2038–42. http://dx.doi.org/10.1103/physreve.47.2038.

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32

Kircher, R., and W. Bergner. "Modeling of Charge Conservation in Isolated Silicon Regions." Japanese Journal of Applied Physics 28, Part 1, No. 12 (December 20, 1989): 2454–58. http://dx.doi.org/10.1143/jjap.28.2454.

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33

Kouw, L. R., and H. P. Blok. "The one-body current operator and charge conservation." Physics Letters B 164, no. 4-6 (December 1985): 203–6. http://dx.doi.org/10.1016/0370-2693(85)90309-0.

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34

Villasenor, John, and Oscar Buneman. "Rigorous charge conservation for local electromagnetic field solvers." Computer Physics Communications 69, no. 2-3 (March 1992): 306–16. http://dx.doi.org/10.1016/0010-4655(92)90169-y.

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35

Snider, A. D. "Charge conservation and the transcapacitance element: an exposition." IEEE Transactions on Education 38, no. 4 (1995): 376–79. http://dx.doi.org/10.1109/13.473160.

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36

Changshi, Liu. "Energy and charge conservation during photo capacitance-voltage." Energy 214 (January 2021): 118899. http://dx.doi.org/10.1016/j.energy.2020.118899.

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37

Barthelmé, Régine. "Conservation de la charge dans les codes PIC." Comptes Rendus Mathematique 341, no. 11 (December 2005): 689–94. http://dx.doi.org/10.1016/j.crma.2005.09.008.

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38

Lee, H., J. K. Woo, and S. Kim. "CMOS differential-capacitance-to-frequency converter utilising repetitive charge integration and charge conservation." Electronics Letters 46, no. 8 (2010): 567. http://dx.doi.org/10.1049/el.2010.3416.

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39

Eisenberg, Bob, Xavier Oriols, and David Ferry. "Dynamics of Current, Charge and Mass." Computational and Mathematical Biophysics 5, no. 1 (October 26, 2017): 78–115. http://dx.doi.org/10.1515/mlbmb-2017-0006.

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Abstract Electricity plays a special role in our lives and life. The dynamics of electrons allow light to flow through a vacuum. The equations of electron dynamics are nearly exact and apply from nuclear particles to stars. These Maxwell equations include a special term, the displacement current (of a vacuum). The displacement current allows electrical signals to propagate through space. Displacement current guarantees that current is exactly conserved from inside atoms to between stars, as long as current is defined as the entire source of the curl of the magnetic field, as Maxwell did.We show that the Bohm formulation of quantum mechanics allows the easy definition of the total current, and its conservation, without the dificulties implicit in the orthodox quantum theory. The orthodox theory neglects the reality of magnitudes, like the currents, during times that they are not being explicitly measured.We show how conservation of current can be derived without mention of the polarization or dielectric properties of matter. We point out that displacement current is handled correctly in electrical engineering by ‘stray capacitances’, although it is rarely discussed explicitly. Matter does not behave as physicists of the 1800’s thought it did. They could only measure on a time scale of seconds and tried to explain dielectric properties and polarization with a single dielectric constant, a real positive number independent of everything. Matter and thus charge moves in enormously complicated ways that cannot be described by a single dielectric constant,when studied on time scales important today for electronic technology and molecular biology. When classical theories could not explain complex charge movements, constants in equations were allowed to vary in solutions of those equations, in a way not justified by mathematics, with predictable consequences. Life occurs in ionic solutions where charge is moved by forces not mentioned or described in the Maxwell equations, like convection and diffusion. These movements and forces produce crucial currents that cannot be described as classical conduction or classical polarization. Derivations of conservation of current involve oversimplified treatments of dielectrics and polarization in nearly every textbook. Because real dielectrics do not behave in that simple way-not even approximately-classical derivations of conservation of current are often distrusted or even ignored. We show that current is conserved inside atoms. We show that current is conserved exactly in any material no matter how complex are the properties of dielectric, polarization, or conduction currents. Electricity has a special role because conservation of current is a universal law.Most models of chemical reactions do not conserve current and need to be changed to do so. On the macroscopic scale of life, conservation of current necessarily links far spread boundaries to each other, correlating inputs and outputs, and thereby creating devices.We suspect that correlations created by displacement current link all scales and allow atoms to control the machines and organisms of life. Conservation of current has a special role in our lives and life, as well as in physics. We believe models, simulations, and computations should conserve current on all scales, as accurately as possible, because physics conserves current that way. We believe models will be much more successful if they conserve current at every level of resolution, the way physics does.We surely need successful models as we try to control macroscopic functions by atomic interventions, in technology, life, and medicine. Maxwell’s displacement current lets us see stars. We hope it will help us see how atoms control life.
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40

Zeng Jun, 曾军, and 李晋红 Li Jinhong. "Distance for Conservation of Topological Charge in Atmospheric Turbulence." Acta Optica Sinica 35, s1 (2015): s101005. http://dx.doi.org/10.3788/aos201535.s101005.

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41

Okun', L. B. "Tests of electric charge conservation and the Pauli principle." Uspekhi Fizicheskih Nauk 158, no. 6 (1989): 293. http://dx.doi.org/10.3367/ufnr.0158.198906d.0293.

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42

Brading, Katherine A. "Which symmetry? Noether, Weyl, and conservation of electric charge." Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 33, no. 1 (March 2002): 3–22. http://dx.doi.org/10.1016/s1355-2198(01)00033-8.

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43

Munz, Claus-Dieter, Rudolf Schneider, Eric Sonnendrücker, and Ursula Voss. "Maxwell's equations when the charge conservation is not satisfied." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 328, no. 5 (March 1999): 431–36. http://dx.doi.org/10.1016/s0764-4442(99)80185-2.

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44

Singh, Ravindra P., and Sanjoy Roychowdhury. "Non-conservation of topological charge: Experiment with optical vortex." Journal of Modern Optics 51, no. 2 (January 2004): 177–81. http://dx.doi.org/10.1080/09500340408235262.

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45

Okun', Lev B. "Tests of electric charge conservation and the Pauli principle." Soviet Physics Uspekhi 32, no. 6 (June 30, 1989): 543–47. http://dx.doi.org/10.1070/pu1989v032n06abeh002727.

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46

Maslov, V. P. "Super-second quantisation and entropy quantisation with charge conservation." Russian Mathematical Surveys 55, no. 6 (December 31, 2000): 1157–58. http://dx.doi.org/10.1070/rm2000v055n06abeh000347.

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47

Silver, G. L. "Charge conservation applied to experimental data for plutonium solutions." Journal of Radioanalytical and Nuclear Chemistry 314, no. 3 (November 7, 2017): 1523–26. http://dx.doi.org/10.1007/s10967-017-5601-7.

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48

Norman, Eric B., John N. Bahcall, and Maurice Goldhaber. "Improved limit on charge conservation derived fromGa71solar neutrino experiments." Physical Review D 53, no. 7 (April 1, 1996): 4086–88. http://dx.doi.org/10.1103/physrevd.53.4086.

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49

Dolgov, A. D., and V. A. Novikov. "CPT, Lorentz invariance, mass differences, and charge non-conservation." JETP Letters 95, no. 11 (August 2012): 594–97. http://dx.doi.org/10.1134/s0021364012110033.

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50

Keil, Robert, Changsuk Noh, Amit Rai, Simon Stützer, Stefan Nolte, Dimitris G. Angelakis, and Alexander Szameit. "Optical simulation of charge conservation violation and Majorana dynamics." Optica 2, no. 5 (May 5, 2015): 454. http://dx.doi.org/10.1364/optica.2.000454.

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