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Waves, shocks and symmetrization in a nonlinear theory of electrodynamics

ВОлНы, УДАРНыЕ ВОлНы И сИММЕтРИжАцИь В НЕлИ НЕИНОИ тЕОРИИ ЁлЕктРОДИНАМ ИкИ

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Il Nuovo Cimento A (1965-1970)

Summary

Within the context of a nonlinear formulation of electrodynamics based on the constraintA 2Μ = ϱ2(A Μtimelike) for the electromagnetic potentialA Μtogether with the usual gauge-invariant electromagnetic-field Lagrangian, we study the propagation of weak discontinuities and shocks. Further the structure of the system of differential equations for the different fields is briefly examined.

Riassunto

Nellàmbito di una formulazione non lineare dell’elettrodinamica fondata sul vincolo A 2Μ , = ϱ2 A Μdi tipo tempo) per il potenziale elettromagneticoA Μ insieme all’usuale Lagrangiana invariante di gauge per il campo elettromagnetico, si studia la propagazione di discontinuità deboli e di urti. Si esamina inoltre brevemente la struttura del sistema di equazioni differenziali per i diversi campi.

РЕжУМЕ

В РАМкАх НЕлИНЕИНОИ Ф ОРМУлИРОВкИ ЁлЕктРОДИНАМИкИ, ОсН ОВАННОИ НА ОгРАНИЧЕНИИA 2μ =-ϱ2 (АΜ ь ВльЕтсь ВРЕМЕНИпОДО БНыМ) Дль ЁлЕктРОМАгНИтНОгО пОтЕНцИАлА АΜ, ВМЕстЕ с ОБыЧНыМ лАгРАНжИАН ОМ кАлИБРОВОЧНО ИНВАРИ АНтНОгО ЁлЕктРОМАгНИтНОгО п Оль, Мы ИсслЕДУЕМ РАсп РОстРАНЕНИЕ слАБых РАжРыВОВ И УДА РНых ВОлН. РАссМАтРИВАЕтс ь стРУктУРА сИстЕМы ДИФФЕРЕНцИАльНых УР АВНЕНИИ Дль РАжлИЧНы х пОлЕИ.

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References

  1. P. A. M. Dirac:Proc. B. Soc. London, Ser. A,209, 292 (1951);212, 330 (1952);223, 438 (1954). Let us note that Dieac initially took the electromagnetic potential as proportional to the current velocity four-vector and never searched for particlelike solutions to the equations of motion as is done in ref. (4,5).

    MathSciNet  ADS  Google Scholar 

  2. E. Schrödinger:Nature (London),169, 538 (1952).

    Article  ADS  MATH  Google Scholar 

  3. R. Righi andG. Venturi:Int. J. Theor. Phys.,21, 63 (1982).

    Article  MathSciNet  Google Scholar 

  4. R. Eighi andG. Venturi:Lett. Nuovo Cimento,31, 487 (1981).

    Article  Google Scholar 

  5. P. Garbaczewski:J. Math. Phys. (N. Y.),24, 341 (1983).

    Article  MathSciNet  ADS  Google Scholar 

  6. Y. Nambu:Prog. Theor. Phys. Suppl., Extra Number, 190 (1968).

  7. G. Boillat:J. Math. Phys. (N. Y.),11, 941 (1970);Phys. Lett. A,38, 181 (1972);C. R. Acad. Sci. Ser. A,290, 259 (1982).

    Article  ADS  Google Scholar 

  8. M. Born andL. Infeld:Proc. R. Soc. London, Ser. A,144, 425 (1934).

    Article  ADS  Google Scholar 

  9. T. Ruggeri andA. Strumia:Ann. Inst. Henri Poincaré Ser. A,34, 65 (1981), and references therein.

    MathSciNet  MATH  Google Scholar 

  10. G. Boillat:C.R. Acad. Sci. Ser. I, 551 (1982).

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Authors and Affiliations

  1. Istituto di Matematica Applicata dell’Università, Bologna, Italia

    G. Boillat

  2. Istituto di Fisica dell’ Università, Bologna

    G. Venturi

  3. Sezione di Bologna, Italia Istituto Nazionale di Fisica Nucleare, Italia

    G. Venturi

  4. Département de Mathématiques, Université de Clermont, Clermont-Ferrand, France

    G. Boillat

Authors
  1. G. Boillat
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  2. G. Venturi
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Boillat, G., Venturi, G. Waves, shocks and symmetrization in a nonlinear theory of electrodynamics. Nuov Cim A 77, 358–367 (1983). https://doi.org/10.1007/BF02816661

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  • DOI: https://doi.org/10.1007/BF02816661

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