Summary
We pursue the renewed interest in string or embedding model for general relativity. Our theory is free of the objections raised by Deseret al., because it takes the embedding space seriously as the arena for physics. We consider a classical space-timeV 4 as a minimal surface in a curved embedding spaceV N. Matter onV 4 comes from the curvature ofV n. Two versions of the covariant canonical formalisms for minimal surfaces are then developed. They avoid the difficulties of the Dixac constraint formalism; this is achieved by properly modifying the very important approach by Bund. Our canonical formalisms can be used also for relativistic strings or membranes.
Riassunto
Si porta avanti il rinnovato interesse per il modello della stringa o di inclusione nella relatività generale. La nostra teoria non è suscettibile delle obiezioni sollevate da Deseret al., perchè considera seriamente lo spazio di inclusione come arena per la flsica. Si considera uno spazio-tempo classicoV 4 come superficie minima in uno spazio di inclusione curvoV n. La materia suV 4 deriva dalla curvatura diV N. Si sviluppano quindi due versioni dei formalismi covarianti canonici per le superfici minime. Questi evitano le difficoltà del formalismo del vincolo di Dirac; ciò si ottiene modificando opportunamente l’approccio molto importante di Rund. I nostri formalismi canonici si possono usare anche per le stringhe relativistiche o membrane.
РЕжУМЕ
Мы жАНОВО РАссМАтРИВ АЕМ стРУННУУ МОДЕль Д ль ОБЩЕИ тЕОРИИ ОтНОсИт ЕльНОстИ. НАшА тЕОРИь сВОБОДНА От ВОжРАжЕНИИ, ВыДВИН Утых ДЕжЕРОМ И ДР., т.к. В ЁтОИ тЕОРИИ ВНЕДР ЕННОЕ пРОстРАНстВО пРЕДстАВльЕт АРЕНУ Д ль ФИжкИ. Мы РАссМАтРИВАЕМ клАсс ИЧЕскОЕ пРОстРАНстВ О-ВРЕМьV 4, кАк МИНИМАльНУУ пОВЕ РхНОсть В ИскРИВлЕННОМ ВНЕДР ЕННОМ пРОстРАНстВЕ VN. ВЕЩЕстВО НАV 4 ВОжНИкАЕт Иж кРИВ ИжНы VN. жАтЕМ РАжВИВАУтсь Д ВА ВАРИАНтА кОВАРИАН тНых кАНОНИЧЕскИх ФОРМАл ИжМОВ Дль МИНИМАльНых пОВЕ РхНОстЕИ. ЁтИ пОДхОДы пОжВОльУт ОБОИтИ тРУДНОстИ ДИРАкОВскОгО ФОРМАл ИжМА ОгРАНИЧЕНИИ. НАш кАНОНИЧЕскИИ ФОРМАл ИжМ МОжЕт Быть тАкжЕ ИспОльжОВАН Дл ь РЕльтИВИстскИх стР УН ИлИ МЕМБРАН.
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Pavšič, M. String model for general relativity and canonical formalism for minimal surfaces. Nuov Cim A 95, 297–310 (1986). https://doi.org/10.1007/BF02906446
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DOI: https://doi.org/10.1007/BF02906446