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Abstract:

The Born-Infeld equation in the plane is usefully captured in complex language. The general exact solution can be written as a combination of holomorphic and anti-holomorphic functions. However, this solution only expresses the potential in an implicit way. We rework the formulation to obtain the complex potential in an explicit way, by means of a perturbative procedure. We take care of the secular behavior common to this kind of approach, by resorting to a symmetry the equation has at the considered order of approximation. We apply the method to build approximated solutions to Born-Infeld electrodynamics. We solve for BI electromagnetic waves traveling in opposite directions. We study the propagation at interfaces, with the aim of searching for effects susceptible to experimental detection. In particular, we show that a reflected wave is produced when a wave is incident on a semi-space containing a magnetostatic field. © 2016, The Author(s).

Registro:

Documento: Artículo
Título:Approximated solutions to Born-Infeld dynamics
Autor:Ferraro, R.; Nigro, M.
Filiación:Instituto de Astronomía y Física del Espacio (IAFE, CONICET-UBA), Casilla de Correo 67, Sucursal 28, Buenos Aires, 1428, Argentina
Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, Buenos Aires, 1428, Argentina
Palabras clave:Integrable Equations in Physics; Integrable Field Theories
Año:2016
Volumen:2016
Número:2
Página de inicio:1
Página de fin:14
DOI: http://dx.doi.org/10.1007/JHEP02(2016)002
Título revista:Journal of High Energy Physics
Título revista abreviado:J. High Energy Phys.
ISSN:11266708
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_11266708_v2016_n2_p1_Ferraro

Referencias:

  • Born, M., Infeld, L., Foundations of the new field theory (1934) Proc. Roy. Soc. Lond., A 144, p. 425. , [INSPIRE]
  • Born, M., Infeld, L., Foundations of the new field theory (1933) Nature, 132, p. 1004
  • Born, M., Quantum theory of the electromagnetic field (1934) Proc. Roy. Soc. Lond., A 143, p. 410. , [INSPIRE]
  • M. Born and L. Infeld, On the quantization of the new field equations. I, Proc. Roy. Soc. Lond. A 147 (1934) 522; Fradkin, E.S., Tseytlin, A.A., Nonlinear electrodynamics from quantized strings (1985) Phys. Lett., B 163, p. 123. , [INSPIRE]
  • Abouelsaood, A., Callan, C.G., Jr., Nappi, C.R., Yost, S.A., Open strings in background gauge fields (1987) Nucl. Phys., B 280, p. 599. , [INSPIRE]
  • Leigh, R.G., Dirac-Born-Infeld action from Dirichlet σ-model (1989) Mod. Phys. Lett., A 4, p. 2767. , [INSPIRE]
  • Metsaev, R.R., Rakhmanov, M., Tseytlin, A.A., The Born-Infeld action as the effective action in the open superstring theory (1987) Phys. Lett., B 193, p. 207. , [INSPIRE]
  • Tseytlin, A.A., On non-Abelian generalization of Born-Infeld action in string theory (1997) Nucl. Phys., B 501, p. 41. , [hep-th/9701125] [INSPIRE]
  • J. Plebanski, Lectures on non linear electrodynamics, Nordita Lecture Notes, Copenhagen Denmark (1968); Boillat, G., Nonlinear electrodynamics-Lagrangians and equations of motion (1970) J. Math. Phys., 11, p. 941. , [INSPIRE]
  • Deser, S., Puzalowski, R., Supersymmetric nonpolynomial vector multiplets and causal propagation (1980) J. Phys., A 13, p. 2501. , [INSPIRE]
  • I. Bialynicki-Birula, Nonlinear electrodynamics: variations on a theme by Born and Infeld, in J. Lopuszanski’s Festschrift, Quantum Theory of Particles and Fields, B. Jancewicz and J. Lukierski eds., World Scientific, Singapore (1983), pg. 31; R. Kerner, A.L. Barbosa and D.V. Gal’tsov, Topics in Born-Infeld electrodynamics, in Proceedings of XXXVII Karpacz Winter School, J. Lukierski and J. Rembielinski eds., Amer. Math. Soc., Providence U.S.A. (2001) [AIP Conf. Proc. 589 (2001) 377]; Brenier, Y., Hydrodynamic structure of the augmented Born-Infeld equations (2004) Arch. Rat. Mech. Anal., 172, p. 65
  • Kiessling, M.K.H., Convergent perturbative power series solution of the stationary Maxwell-Born-Infeld field equations with regular sources (2011) J. Math. Phys., 52, p. 022902. , [INSPIRE]
  • Kiessling, M.K.-H., Some uniqueness results for stationary solutions to the Maxwell-Born-Infeld field equations and their physical consequences (2011) Phys. Lett., A 375, p. 3925
  • Pryce, M.H.L., The two-dimensional electrostatic solutions of Born’s new field equations (1935) Proc. Cambr. Phil. Soc., 31, p. 50
  • Pryce, M.H.L., On a uniqueness theorem (1935) Proc. Cambr. Phil. Soc., 31, p. 625
  • Ferraro, R., 2D Born-Infeld electrostatic fields (2004) Phys. Lett., A 325, p. 134. , [hep-th/0309185] [INSPIRE]
  • Ferraro, R., Lipchak, M.E., Born-Infeld corrections to Coulombian interactions (2008) Phys. Rev., E 77, p. 046601. , [hep-th/0609141] [INSPIRE]
  • Ferraro, R., Born-Infeld electrostatics in the complex plane (2010) JHEP, 12, p. 028. , [arXiv:1007.2651] [INSPIRE]
  • Ferraro, R., Two-dimensional solutions for Born-Infeld fields (2013) JHEP, 8, p. 048. , [arXiv:1304.5506] [INSPIRE]
  • Kobayashi, O., Maximal surfaces in the 3-dimensional Minkowski space L3 (1983) Tokyo J. Math., 6, p. 297
  • M. Bordemann and J. Hoppe, The dynamics of relativistic membranes 2. Nonlinear waves and covariantly reduced membrane equations, Phys. Lett. B 325 (1994) 359; Barbashov, B.M., Chernikov, N.A., The possibility of an oscillatory nature of gravitational collapse (1967) Sov. Phys. JETP, 24, p. 437
  • Ibarguen, H.S., García, A., Plebanski, J., Signals in nonlinear electrodynamics invariant under duality rotations (1989) J. Math. Phys., 30, p. 2689. , [INSPIRE]
  • M. Novello, V.A. De Lorenci, J.M. Salim and R. Klippert, Geometrical aspects of light propagation in nonlinear electrodynamics, Phys. Rev. D 61 (2000) 045001; Ferraro, R., Testing Born-Infeld electrodynamics in waveguides (2007) Phys. Rev. Lett., 99, p. 230401. , [arXiv:0710.3552] [INSPIRE]
  • Aiello, M., Bengochea, G., Ferraro, R., Anisotropic effects of background fields on Born-Infeld electromagnetic waves (2007) Phys. Lett., A 361, p. 9. , [hep-th/0607072] [INSPIRE]
  • Ferraro, R., Testing nonlinear electrodynamics in waveguides: the effect of magnetostatic fields on the transmitted power (2010) J. Phys., A 43, p. 195202. , [INSPIRE]
  • Petrov, E.Y., Kudrin, A.V., Exact self-similar solutions in Born-Infeld theory (2013) Phys. Rev., D 87, p. 087703. , [arXiv:1302.4353] [INSPIRE]
  • Burton, D.A., Trines, R.M.G.M., Walton, T.J., Wen, H., Exploring Born-Infeld electrodynamics using plasmas (2011) J. Phys., A 44, p. 095501. , [arXiv:1006.2246] [INSPIRE]
  • Schellstede, G.O., Perlick, V., Lämmerzahl, C., Testing non-linear vacuum electrodynamics with Michelson interferometry (2015) Phys. Rev., D 92, p. 025039. , [arXiv:1504.03159] [INSPIRE]

Citas:

---------- APA ----------
Ferraro, R. & Nigro, M. (2016) . Approximated solutions to Born-Infeld dynamics. Journal of High Energy Physics, 2016(2), 1-14.
http://dx.doi.org/10.1007/JHEP02(2016)002
---------- CHICAGO ----------
Ferraro, R., Nigro, M. "Approximated solutions to Born-Infeld dynamics" . Journal of High Energy Physics 2016, no. 2 (2016) : 1-14.
http://dx.doi.org/10.1007/JHEP02(2016)002
---------- MLA ----------
Ferraro, R., Nigro, M. "Approximated solutions to Born-Infeld dynamics" . Journal of High Energy Physics, vol. 2016, no. 2, 2016, pp. 1-14.
http://dx.doi.org/10.1007/JHEP02(2016)002
---------- VANCOUVER ----------
Ferraro, R., Nigro, M. Approximated solutions to Born-Infeld dynamics. J. High Energy Phys. 2016;2016(2):1-14.
http://dx.doi.org/10.1007/JHEP02(2016)002