Summary
We study, un.der the full action of gauge invariancc including two Itiggs phenomena, Weyl’s gauge model coupled to a Higgs field. As a result, we obtain the coupled Einsteia- Weyl field equations with the cosmological constant, which are analogous to the Einstein-Maxwell equations apart from difficulties inherent to Weyl’s geometry. The vacuum solution of a Higgs field will be discussed in connection with a manifestly gaugc-invariant formulation of the Lagrangian density of gravitation. A generalized action which is a function of the gauge-invariant scalar curvature is examined.
Riassunto
Si studia, so,to l’azione piena dell’invarianza di gauge che include due fenomeni di Higgs, il modello di gauge di Weyl accoppiato ad un campo di Higgs. Come risultato si ottengono le equazioni di campo accoppiate di Einstein-Weyl con la costante cosmologica, che sono analoghe alle equazioni di Einstein-Maxwell tranne per difficoltà inerenti alia gcometria di Weyl. La soluzione nel vuoto di un campo di Higgs sarà discussa in connessione con una formulazione palesemente invariante di gauge della densità lagrangiana di gravitazione. Si esamina un’azione generalizzata che è funzione della curvatura sealare invariante di gauge.
Резюме
Мы зсследуем калнбро вочную модель Вейля, с вязанную с нолем Хзггса. Хы нолучаем св язаннъше нолевые ура внензя Эйнгнтейна-Ве йля с космо-логзческо й ностоянной, которые а налогзчнъш уравненз ям ЭйнШтейна-Максвел ла, за нсключензем трудн остей, нрзсупгнх геом етрзз Вейля. Вакуумно е реншензе для ноля Хзтгса обсуж-дае тся в связз с явной кал збровочно знварз-ант ной формулз-ровкой нлотностз Лагранжза на для гравзтаЦзз. Исс ледуется обобшЦенно е дейст-взе, которое является фун кЦзей калзбровочно з нварзантной скалярн ой крзвззнъш.
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Nishioka, M. The coupled einstein-weyl field equations with cosmological constant and role of two higgs phenomena in weyl’s gauge model coupled to a higgs field. Nuov Cim A 78, 462–470 (1983). https://doi.org/10.1007/BF02962241
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DOI: https://doi.org/10.1007/BF02962241