Il Nuovo Cimento A (1965-1970)

, Volume 43, Issue 2, pp 145–151 | Cite as

A nonlinear approach to classical electrodynamics

  • R. Righi
  • G. Venturi


A nonlinear approach to classical electrodynamics is presented. On imposing a nonlinear-gauge choice, together with the usual gauge-invariant electromagnetic-field Lagrangian, it is found that the resulting equations of motion have static, spherically symmetric, extended solutions which may be regarded as charged particles. Indeed, in the presence of a small perturbation, the effective Hamiltonian obtained is the same as that of a charged spherical shell with radius that of the corresponding classical charged particle, in an electromagnetic field. Further one finds a conserved topological current whose associated conserved charge is proportional to the charged-particle number.

Нелинейный подход к классической злектродинамике


Предлагается нелинейный подход к классической злектродинамике. Испольэуя нелинейную калибровку, вместе с обычным калибровочно инвариантным Лагранжианом злектромагнитного поля, получается, что окончательные уравнения движения имеют статические, сферически симметричные протяженные рещения, которые могут рассматриваться как эаряженные частицы. При наличии малого воэмушения полученный зффективный Гамильтониан является таким же, как для случая эаряженной сферической оболочки с радиусом, который соответствует классической эаряженной частице в злектромагнитном поле. Также определяется сохраняюшийся топологический ток, причем, сохраняюшийся эаряд, свяэанный с зтим током, пропорционален числу эаряженных частиц.


Si presenta un approccio non lineare all’elettrodinamica classica. Imponendo una scelta di gauge non lineare, insieme con l’usuale Lagrangiana invariante per trasformazioni di gauge per il campo elettromagnetico, si trova che le risultanti equazioni del moto hanno soluzioni estese, statiche, e a simmetria sferica che possono essere considerate come particelle cariche. Infatti, in presenza di una piccola perturbazione, la Hamiltoniana effettiva ottenuta è la stessa che per un guscio sferico carico, avente raggio uguale a quello della corrispondente particella carica classica, in un campo elettromagnetico. Si trova inoltre una corrente topologica conservata la cui carica conservata è proporzionale al numero di particelle cariche.


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Copyright information

© Società Italiana di Fisica 1978

Authors and Affiliations

  • R. Righi
    • 1
    • 2
  • G. Venturi
    • 1
    • 2
  1. 1.Istituto di Fisica dell’UniversitàBologna
  2. 2.Istituto Nazionale di Fisica NucleareSezione di BolognaItaly

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