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Cartan spinors, minimal surfaces and strings

Спиноры Картана, минимальные поверхности и струны

  • Published:
Il Nuovo Cimento B (1971-1996)

Summary

The geometry of the Enneper-Weierstrass representation and of the Gauss map of minimal surfaces inR 4 is analysed in terms of holomorphic spinor fields. The restriction to Majorana spinors and some representation of strings inR 3,1 is studied. The analogy of the corresponding Gauss map with Fermi-Yang weak currents (both neutral and charged) is underlined. The geometry of Lorentzian surfaces inR 2,2 is analysed in all generalities and details.

Riassunto

Si analizza la geometria della rappresentazione di Enneper-Weierstrass della mappa di Gauss di superfici minimali inR 4 in termini di campi spinoriali olomorfici. Si studia la restrizione degli spinori di Majorana e qualche rappresentazione di stringhe inR 3,1. Si sottolinea l’analogia della mappa di Gauss corrispondente con le correnti deboli (sia neutre che cariche) di Fermi-Yang. Si analizza sia in generale che in dettaglio la geometria delle superfici lorentziane inR 2,2.

Резюме

Геометрия представления Эннепера-Вейерщтрасса и гауссова отображения минимальных поверхностей вR 4 анализируется в терминах голоморфных спинорных полей. Исследуются ограничения на спиноры Майораны и на некоторые представления струн вR 3,1. Отмечается аналогия между соответствующих гауссовым отображением и слабыми (нейтральными и заряженными) токами Ферми-Янга. Подробно анализируется геометрия лоренцевых поверхностей вR 2,2.

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Authors and Affiliations

  1. International School for Advanced Studies, Strada Costiera 11, 34014, Trieste, Italia

    P. Budinich

  2. International Center for Theoretical Physics, Strada Costiera 11, 34014, Trieste, Italia

    M. Rigoli

Authors
  1. P. Budinich
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  2. M. Rigoli
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Budinich, P., Rigoli, M. Cartan spinors, minimal surfaces and strings. Nuov Cim B 102, 609–647 (1988). https://doi.org/10.1007/BF02725619

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