Summary
Theλϕ 4 model and the pendulum sine-Gordon equation are systematically studied in a general context with various boundary conditions, so that solutions can be viewed in a broader perspective. The kink and soliton solutions are seen to arise only under specific conditions when elliptic functions degenerate into circular functions. Other elementary functional interactions that may be of relevance to the description of hadrons, such as theλϕ n model, the cos, sinh, cosh and exponential equations, are proposed, and exact solutions are obtained.
Riassunto
Si studiano sistematicamente il modelloλϕ 4 e l’equazione di sine-Gordon del pendolo in un contesto generale con varie condizioni di limite, in modo tale che le soluzioni possono essere viste in una prospettiva più ampia. Le soluzioni del solitone e del kink sono viste formarsi solo in condizioni specifiche quando le funzioni ellittiche degenerano in funzioni circolari. Si propagano altre interazioni funzionali elementari che possono essere importanti per la descrizione il cos, il sinh, il cosh e esponenziali, e si ottengono soluzioni esatte.
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Reference
For a review, see the excellent 1975 Erice lectures delivered byS. Coleman:Classical lumps and their quantum descendants.
G. Petiau: inApplications des equations non-linéaires à la physique théorique (Editions de laRevue d’Optique Théorique et Instrumentale (Paris, 1962), p. 127).
B. Hu:Fermions as solitons, Ecole Polytechnique preprint (to be published).
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Hu, B. Generalizing the pendulum sine-gordon equation and its solutions. Nuov Cim A 38, 441–454 (1977). https://doi.org/10.1007/BF02730015
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DOI: https://doi.org/10.1007/BF02730015