zbMATH — the first resource for mathematics

Analytical calculation of stored electrostatic energy per unit length for an infinite charged line and an infinitely long cylinder in the framework of Born-Infeld electrostatics. (English) Zbl 1433.78005
Summary: More than 80 years ago, Born-Infeld electrodynamics was proposed in order to remove the point charge singularity in Maxwell electrodynamics. In this work, after a brief introduction to Lagrangian formulation of Abelian Born-Infeld model in the presence of an external source, we obtain the explicit forms of Gauss’s law and the energy density of an electrostatic field for Born-Infeld electrostatics. The electric field and the stored electrostatic energy per unit length for an infinite charged line and an infinitely long cylinder in Born-Infeld electrostatics are calculated. Numerical estimations in this paper show that the nonlinear corrections to Maxwell electrodynamics are considerable only for strong electric fields. We present an action functional for Abelian Born-Infeld model with an auxiliary scalar field in the presence of an external source. This action functional is a generalization of the action functional which was presented by A. A. Tseytlin [Nucl. Phys., B 469, No. 1–2, 51–67 (1996; Zbl 1002.81537)] in his studies on low energy dynamics of \(D\)-branes. Finally, we derive the symmetric energy-momentum tensor for Abelian Born-Infeld model with an auxiliary scalar field.

78A30 Electro- and magnetostatics
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
78A25 Electromagnetic theory, general
Full Text: DOI arXiv
[1] Born, M.; Infeld, L., Foundations of the new field theory, Proceedings of the Royal Society of London A, 144, 425, (1934) · JFM 60.0750.02
[2] Fortunato, D.; Orsina, L.; Pisani, L., Born-Infeld type equations for electrostatic fields, Journal of Mathematical Physics, 43, 11, 5698-5706, (2002) · Zbl 1060.78004
[3] Mazharimousavi, S. H.; Halilsoy, M., Ground state H-atom in born-infeld teory, Foundations of Physics, 42, 4, 524-530, (2012) · Zbl 1242.81147
[4] De Assis, L. P.; Gaete, P.; Helayel-Neto, J. A.; Vellozo, S. O., Aspects of magnetic field configurations in planar nonlinear electrodynamics, International Journal of Theoretical Physics, 51, 2, 477-486, (2012) · Zbl 1242.83089
[5] Vad, Z. K., Some solutions of Einstein-Born-Infeld field equations, Acta Physica Hungarica, 63, 3-4, 353-364, (1988)
[6] Gaete, P.; Schmidt, I., Coulomb’s law modification in nonlinear and in noncommutative electrodynamics, International Journal of Modern Physics A, 19, 20, 3427-3437, (2004)
[7] Callan, C. G.; Maldacena, J. M., Brane dynamics from the Born-Infeld action, Nuclear Physics B, 513, 1-2, 198-212, (1998) · Zbl 0958.81105
[8] Gibbons, G. W., Born-Infeld particles and Dirichlet \(p\)-branes, Nuclear Physics. B, 514, 3, 603-639, (1998) · Zbl 0917.53032
[9] Gibbons, G. W., Aspects of born-infeld theory and string/M-theory, Revista Mexicana de Física, 49, 19-29, (2003)
[10] Zwiebach, B., A First Course in String Theory, (2009), Cambridge, UK: Cambridge University Press, Cambridge, UK · Zbl 1185.81005
[11] Lu, H. Q., Phantom cosmology with a nonlinear born-infeld type scalar field, International Journal of Modern Physics D, 14, 2, 355, (2005) · Zbl 1071.83570
[12] Serie, E.; Masson, T.; Kerner, R., Non-abelian generalization of Born-Infeld theory inspired by noncommutative geometry, Physical Review D, 68, 12, (2003)
[13] Hendi, S. H., Asymptotic Reissner–Nordström black holes, Annals of Physics, 333, 282-289, (2013) · Zbl 1284.83060
[14] Gaete, P.; Helayël-Neto, J., Finite field-energy and interparticle potential in logarithmic electrodynamics, The European Physical Journal C, 74, article 2816, (2014)
[15] Gaete, P.; Helayël-Neto, J., Remarks on nonlinear electrodynamics, The European Physical Journal C, 74, 11, article 3182, (2014)
[16] Riazi, N.; Mohammadi, M., Composite lane-emden equation as a nonlinear poisson equation, International Journal of Theoretical Physics, 51, 4, 1276-1283, (2012) · Zbl 1248.78016
[17] Euler, H.; Kockel, B., Über die streuung von licht an licht nach der diracschen theorie, Naturwissenschaften, 23, 15, 246-247, (1935) · Zbl 0011.14106
[18] Euler, H., Ober die Streuung von Licht an Licht nach der Diracschen Theorie, Annalen der Physik (Leipzig), 26, 398-448, (1936) · Zbl 0014.23706
[19] Heisenberg, W.; Euler, H., Folgerungen aus der diracschen theorie des positrons, Zeitschrift für Physik, 98, 11-12, 714-732, (1936) · Zbl 0013.18503
[20] Ruffini, R.; Wu, Y.-B.; Xue, S.-S., Einstein-Euler-Heisenberg theory and charged black holes, Physical Review D, 88, (2013)
[21] Accioly, A., Energy and momentum for the electromagnetic field described by three outstanding electrodynamics, American Journal of Physics, 65, 9, 882-887, (1997)
[22] Soff, G.; Rafelski, J.; Greiner, W., Lower bound to limiting fields in nonlinear electrodynamics, Physical Review A, 7, 3, 903-907, (1973)
[23] Davila, J. M.; Schubert, C.; Trejo, M. A., Photonic processes in Born-Infeld theory, International Journal of Modern Physics A. Particles and Fields. Gravitation. Cosmology, 29, (2014) · Zbl 1306.81310
[24] Halliday, D.; Resnick, R.; Walker, J., Fundamentals of Physics Extended, (2014), Wiley
[25] Costa, C. V.; Gitman, D. M.; Shabad, A. E., Finite field-energy of a point charge in QED
[26] Kruglov, S. I., A model of nonlinear electrodynamics, Annals of Physics, 353, 299-306, (2015) · Zbl 1343.78001
[27] Kruglov, S. I., Nonlinear arcsin-electrodynamics · Zbl 1339.78003
[28] Tseytlin, A. A., Self-duality of Born-Infeld action and Dirichlet 3-brane of type IIB superstring theory, Nuclear Physics B, 469, 1-2, 51-67, (1996) · Zbl 1002.81537
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.