.

Багатовимірна класична і квантова космологія: Автореф. дис… д-ра фіз.-мат. наук / О.І. Жук, НАН України. Ін-т теорет. фізики ім. М.М.Боголюбова. — К

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IAOe?IIAEUeIA AEAAeAI?ss IAOE OE?A?IE

?INOEOOO OAI?AOE*II? O?CEEE ?i. I.I. AIAIETHAIAA

AEoe Ieaenaiae? ?aaiiae/

OAeE 524.83: 531.51: 530.145

Aaaaoiaei??ia eeane/ia ? eaaioiaa einiieia?y

01.04.02 – oai?aoe/ia o?ceea

Aaoi?aoa?ao aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

aeieoi?a o?ceei-iaoaiaoe/ieo iaoe

Ee?a – 1999

Aeena?oaoe??th ? ?oeiien

?iaioa aeeiiaia a Iaeanueeiio aea?aeoi?aa?neoao? ?i. ?.?. Ia/ieeiaa
I?i?noa?noaa ina?oe Oe?a?ie

Iaoeiaee eiinoeueoaio: aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani?

Aaeaiyi Aaaeei Iiananiae/

Iaeanueeee aea?aeoi?aa?neoao, caa?aeoth/ee eaoaae?ith oai?aoe/ii? o?ceee

Io?oe?ei? iiiiaioe:

aeieoi? o?c.-iao. iaoe Caneaanueeee Ieaa Ai?eniae/, Oa?e?anueeee
aea?aeoi?aa?neoao, noa?oee iaoeiaee ni?a?ia?oiee

aeieoi? o?c.-iao. iaoe, noa?oee iaoeiaee ni?a?ia?oiee Ia?iianueeee
Na?a?e Ethaeiie?iae/, Ano?iiii?/ia iana?aaoi??y Ee?anueeiai
oi?aa?neoaoo ?i. Oa?ana Oaa/aiea , i?ia?aeiee iaoeiaee ni?a?ia?oiee

aeieoi? o?c.-iao. iaoe, noa?oee iaoeiaee ni?a?ia?oiee Neoaiei TH??e
Ieaen?eiae/, ?inoeooo oai?aoe/ii? o?ceee ?i. I.I. Aiaiethaiaa IAI
Oe?a?ie, i?ia?aeiee iaoeiaee ni?a?ia?oiee

I?ia?aeia onoaiiaa:

Aei?i?iiao?ianueeee aea?aeaaiee oi?aa?neoao, o?ce/iee oaeoeueoao
I?i?noa?noaa ina?oe Oe?a?ie, i. Aei?i?iiao?ianuee

Caoeno a?aeaoaeaoueny “_____” _________________1999 ?. i ______ aiaeei?
ia can?aeaii?

niaoe?ae?ciaaii? a/aii? ?aaee Ae 26.191.01 ?inoeoooo oai?aoe/ii? o?ceee
?i. I.I.Aiaiethaiaa IAI Oe?a?ie ca aae?anith: 252143, i. Ee?a, aoe.
Iao?ieia?/ia, 14-A.

C aeena?oaoe??th iiaeia iciaeiieoenue o a?ae?ioaoe? ?inoeoooo
oai?aoe/ii? o?ceee

?i. I.I.Aiaiethaiaa IAI Oe?a?ie ca aae?anith: 252143, i. Ee?a, aoe.
Iao?ieia?/ia, 14-A.

Aaoi?aoa?ao ?ic?neaiee “_____” _________________ 1999 ?.

A/aiee nae?aoa?

niaoe?ae?ciaaii? a/aii? ?aaee _____________________
Eocueie/aa A.?.

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue oaie.

Aaaaoiaei??ia einiieia?y – oea iiaee iai?yiie a iaooe? i?i aeieeiaiiy
? aaiethoe?th Anana?oo, yeee oaeaeei ?icaeaa?oueny. Iniiaia eiai
a?aei?ii?noue a?ae noaiaea?oiiai oyaeaiiy i?i aaiiao??th Anana?oo
iieyaaa a i?eiouaii? i?i oa, ui e?euee?noue aei???a i?inoi?o-/ano ?
a?eueoith, i?ae /ioe?e. I?aenoaaith aeey oaeiai i?aeoiaeo noaa
ao?oeeaee ?icaeoie oai??e ia’?aeiaiiy ooiaeaiaioaeueieo aca?iiae?e –
no?oi, noia?no?oi e o.?., ye? iathoue iaea?eueo ocaiaeaeaia
oi?ioethaaiiy naia o i?inoi??-/an? c e?euee?noth aei???a a?eueoa, i?ae
/ioe?e. Iaiao?aeii cacia/eoe, ui, a i?eioeei?, aea/aiiy aaaaoiaei??ii?
einiieia?? iiaeii aeeiioaaoe e aaca?aeiinii aei iineeaiue ia no?oii?
oai???, yeui noaaeoe ia?aae niaith caaea/o iiaoaeiae niinoa??aa?ii?
ea?oeie na?oo ca i?eiouaiiyi ?nioaaiiy aeiaeaoeiaeo aei???a. ?ioeie
neiaaie, ocaaaeueieoe a?aeii? iiaeae? O??aeiaia, Eacia?a ? aea N?ooa?a
ia aaaaoiaei??iee aeiaaeie ?, ii/eiath/e c ia?a?niiai noaio, eiee on?
aei??e aoee ??aiii?aai?, i?eeoe aei yoaeoeaii /ioe?eaei??iiai no/aniiai
Anana?oo. A aeena?oaoe?? aeiaaaeaia i?eioeeiiaa iiaeeea?noue oaeiai
i?aeoiaeo. Iieacaii, /oi iiaeeeai iiaoaeoaaoe oae? iiaeae?, a ?aieao
eio?eo ciai?oi?e (iao) i?ino?? o oiae? aaiethoe?? Anana?oo cacia?
?icoe?aiiy, a aioo??oi? i?inoi?e caeeoathoueny noaa?eueii
eiiiaeoeo?eiaaieie iaaeiei ieaie?anueeeo ianooaa?a, ui i?eaiaeeoue aei
yoaeoeaii /ioe?eaei??iiai Anana?oo.

?aaoey?i? aeine?aeaeaiiy o oeueiio iai?yieo ii/aeenue a?ey 15 ?ie?a oiio
? aoee ni?e/eiai? cia/iei i?ia?anii o iiaoaeia? no?oiieo ?
noia?no?oiieo oai??e. ?aeay i?i aaaaoiaei??i?noue i?inoi?o-/ano aoea
aeneiaeaia a aeaaaeoeyoeo ?ieao o i?iia?nueeeo ?iaioao Eaeooee ?
Eeaeia. Aea a oeeo oa a ?yae? ianooiieo ?ia?o aeiaeaoeia? aei??e
aeei?enoiaoaaeenue oaeaeoa ye iaoaiaoe/iee o?the aeey io?eiaiiy oai??e
ia’?aeiaiiy o?ce/ieo aca?iiae?e, i?ae ye ?aaeueii ?nioth/? aeiaeaoeia?
eii?aeeiaoe. ?icaeoie no?oiieo oai??e aeicaieea aeyiooe ia aeiaeaoeia?
aei??e ye ia ?aaeuei? ia’?eoe. Oaeee i?aeo?ae i?ea?a aei aeieeiaiiy
aaaaoiaei??ii? einiieia??, o ye?e iiaaae?iea Anana?oo aeine?aeaeo?oueny
c a?aooaaiiyi aeiaeaoeiaeo aei???a. Oe? aeine?aeaeaiiy iathoue
ooiaeaiaioaeueia cia/aiiy ia o?eueee aeey einiieia?? ? ano?io?ceee, aea
? aeey o?ceee aeaiaioa?ieo /anoeiie, ine?eueee, c iaeiiai aieo,
aeathoue iiaeeea?noue aeine?aeaeoaaoe aeiaaeueio oiiieia?/io no?oeoo?o
Anana?oo, eiai aaiethoe?th, a, c ?ioiai aieo, ? iie?aiiii aeey
ia?aa??ee no/anieo oai??e ia’?aeiaiiy ooiaeaiaioaeueieo aca?iiae?e.

. sse iaoa??aeueia aeaea?aei, ?icaeyaeathoueny i?i?iaeueia neaey?ia
iiea, ?aeaaeueia ??aeeia ? einiieia?/ia noaea. ?ioaa?oaaiiy
aaaaoiaei??ieo ??aiyiue Aeiooaeia aeicaiey? aecia/eoe aeeiai?/io
iiaaae?ieo Anana?oo.

Ia?o? ?acoeueoaoe, io?eiai? aaoi?ii o oe?e aaeoc? ni?eueii c
A.Ae.?aauoeii ? A.I.Iaeueieeiaei, aoee iioae?eiaai? a 1989 ?. o noaoo?
[1]. Ia oeueiio aoai? aeine?aeaeaiiy i?iaiaeeeenue o aeaio iai?yieao.
Oea, ii-ia?oa, iiooe iiaeo oi/ieo ?ica’yce?a aeey aeiaaeeo aeia?eueii?
e?eueeino? aioo??oi?o i?inoi??a. A aaniethoi?e a?eueoino? ?ia?o,
iioae?eiaaieo aei oeueiai, ?icaeyaeaeenue oi/i? ?ica’ycee aeey iiaeaeae
c iaeiei aioo??oi?i i?inoi?ii. Ocaaaeueiaiiy ia aeia?eueio e?euee?noue
aioo??oi?o i?inoi??a aea? iiaeeea?noue e?aua c?icoi?oe caeiiii??iino?
iiaaae?iee aaaaoiaei??iiai Anana?oo, a oaeiae aoaeiao aoaeoeaieo
/ioe?eaei??ieo oai??e, ye? aeo?eathoue ?c aaaaoiaei??ieo iiaeaeae.
Ae?oaee iai?yiie aeine?aeaeaiue iieyaaa o eaaiooaaii? oeeo
aaaaoiaei??ieo iiaeaeae ? a?aeooeaii? iiaeo oi/ieo ?ica’yce?a eaaioiaeo
??aiyiue, ui aea? iiaeeea?noue aeine?aeeoe eaaioiao iiaaae?ieo
aaaaoiaei??iiai Anana?oo. Oi/i? ?ica’ycee, iioae?eiaai? o noaoo? [1],
aoee ia?oeie c a?aeiieo aaoi?o oi/ieo ?ica’yce?a ??aiyiue O?ea?a-aea
A?ooa aeey aaaaoiaei??ii? einiieia??. O iiaeaeueoiio aeoeaio
aeine?aeaeaiue aoei ci?uaii a noi?iio iiooeo iiaeaeae, a eio?eo
ciai?oi?e (iao) i?ino?? iiaiaeeoueny ye niinoa??aa?iee Anana?o, oiae? ye
aioo??oi? i?inoi?e ? noaa?eueii eiiiaeoeo?eiaaieie iaaeiei
ieaie?anueeeo ianooaa?a. Aaaeeea?noue oaeeo iiaeaeae iieyaa? o oiio,
ui aiie aoaeoeaii iienothoue niinoa??aa?iee na?o ?, oei naiei,
aeiaiaeyoue i?eioeeiiao iiaeeea?noue ?nioaaiiy aeiaeaoeiaeo aei???a.

Ii?yae c iiaoaeiaith oaeeo iiaeaeae iaiao?aeii anoaiiaeoe, aei yeeo
iane?aee?a, ui iiaee ae niinoa??aaoeny, i?eaiaeeoue ?nioaaiiy
aeiaeaoeiaeo aei???a, ine?eueee naia aenia?eiaioaeueia aeyaeaiiy oeeo
iane?aee?a iiaea neoaeeoe i?aeoaa?aeaeaiiyi ?nioaaiiy aeiaeaoeiaeo
aei???a. C oe??? oi/ee ci?o aacia?a/iee ?ioa?an yaeythoue iia? neaey?i?
/anoeiee- a?aa?oaoe?ei? aeneoiie, ye? caaaa/athoueny o aeai?e
aeena?oaoe??.

A?aee?eooy aeiaeaoeiaeo aei???a, yeui aiii a?aeaoaeaoueny, aoaea iaeiei
?c iaeyne?aa?oeo iaoeiaeo aeinyaiaiue a ?noi??? ethaenoaa.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie ? oaiaie.

Aeine?aeaeaiiy o aeaiiio iai?yieo i?iaiaeeeenue o ?aieao athaeaeaoieo
oai Iaeanueeiai aea?aeaaiiai oi?aa?neoaoo ? 519 “Eiiiaeoeo?eaoe?y
i?inoi?o-/ano o eaaioia?e einiieia??” ? ? 721 “?ioeyoe?eia aaiethoe?y
o aaaaoiaei??i?e eaaioia?e einiieia??”, a oaeiae i?iaeo?a I?iaoeueeiai
iaoeiai-aeine?aeiiai oiaa?eoeoaa (DFG) ? 436 UKR 17 ? ? 436 RUS 113.

Iaoa ? caaea/? aeine?aeaeaiiy.

Iaoith ?iaioe ? iiaoaeiaa ye eeane/ieo, oae ? eaaioiaeo aaaaoiaei??ieo
einiieia?/ieo iiaeaeae, aeine?aeaeaiiy aaiethoe?? Anana?oo ? ?a/iaeie
o Anana?o? a ?aieao oeeo iiaeaeae, iiyniaiiy niinoa??aa?ii? ea?oeie
na?oo c a?aooaaiiyi aeiaeaoeiaeo aei???a ? caaaa/aiiy iane?aee?a
?nioaaiiy aioo??oi?o aei???a, ye? iiaeia aoei ae niinoa??aaoe.

Aeey aeinyaiaiiy oe??? iaoe iaiao?aeii i?iaanoe aeine?aeaeaiiy
eeane/ieo ??aiyiue Aeiooaeia aeey aeine?aeaeoaaieo aaaaoiaei??ieo
einiieia?/ieo iiaeaeae ?, cie?aia, ciaeoe iiaeae?, eio?? iiaeooue aooe
oi/ii ?ica’ycai?, ine?eueee oi/i? ?ica’ycee aeicaieythoue aeaoaeueii
aea/eoe aaiethoe?th iaoiai i?inoi?o, eiiiaeoeo?eaoe?th aioo??oi?o
i?inoi??a ? iiaaaeaieo iaoa??aeueieo iie?a.

Eaaioiaa iiaaae?iea Anana?oo iieno?oueny oaeeueiaith ooieoe??th, ui
caaeiaieueiy? ??aiyiith O?ea?a-aea A?ooa. Oiio aeey aea/aiiy iiaaae?iee
Anana?oo ia eaaioiaiio ??ai? iaiao?aeii i?iaanoe aeine?aeaeaiiy
??aiyiiy O?ea?a-aea A?ooa aeey a?aeiia?aeieo iiaeaeae ? ciaeoe ?o oi/i?
?ica’ycee.

Aei ?yaeo iniiaieo caaaeaiue aeena?oaoe?? a?aeiinyoueny, ii-ia?oa,
iiaoaeiaa iiaeaeae, a yeeo ciai?oi?e i?ino?? aaaea naaa ye
niinoa??aa?iee Anana?o, a aioo??oi?e i?ino?? ? noaa?eueii
eii-iaeoeo?eiaaiei iaaeiei ieaie?anueeeo ianooaa?a (oei naiei, oae?
iiaeae? aoaeoeaii iienothoue niinoa??aa?io ea?oeio na?oo ? aeiaiaeyoue
i?eioeeiiao iiaeeea?noue ?nioaaiiy aeiaeaoeiaeo aei???a), ?, ii-ae?oaa,
caaaa/aiiy iane?aee?a ?nioaaiiy aeiaeaoeiaeo aei???a, ye? iiaee ae
niinoa??aaoeny.

Iaoeiaa iiaecia iaea?aeaieo ?acoeueoao?a.

A aeena?oaoe?? io?eiaii oe?eee ?yae iiaeo oi/ieo ?ica’yce?a aeey
aaaaoiaei??ieo einiieia?/ieo iiaeaeae. *anoeia oeeo ?ica’yce?a ?
ocaaaeueiaiiyi a?aeiieo /ioe?eaei??ieo ?ica’yce?a O??aeiaia, Eacia?a ?
aea N?ooa?a ia aeiaaeie aaaaoiaei??ieo iiaeaeae c aeia?eueiith
e?euee?noth aioo??oi?o i?inoi??a. Iieacaii, ui io?eiai? ?ica’ycee
iiaeia ?icaeoe ia aeaa eeane. Aei ia?oiai eeano a?aeiinyoueny iiaeae?,
a yeeo a?aeaoaa?oueny ?cio?ii?caoe?y iioe?aiiy a a?aie/iiio aeiaaeeo
aaeeeeo aaiiao??e. Aeey ae?oaiai eeano iiaeaeae oa?aeoa?iei ?
caii?iaeoaaiiy aioo??oi?o i?inoi??a o oeueiio aeiaaeeo. A a?aie/iiio
aeiaaeeo iaeeo aaiiao??e ?ica’ycee c iaio eean?a i?yiothoue
aneiioioe/ii aei ocaaaeueiaiiai ?ica’yceo Eacia?a.

-iiaeae? ?c naiiae??th. Iaaaaeaii a?aoiaioe, ye? iieacothoue, ui aeey
aeine?aeaeoaaii? iiaeae? o?ce/iith ne?ae aaaaeaoe iao?eeo ciai?oiueiai
i?inoi?o-/ano o cia?aaeaii? Aeiooaeia, a ia A?aina-Ae?eea, ui ?
aaaeeeaei aianeii a aeoeaio aeeneon?th c oeueiai ieoaiiy. I?eaaaeaii
oi?ioee, ye? aeicaieythoue ia?aoai?thaaoe io?eiai? ?ica’ycee ?c iaeiiai
cia?aaeaiiy o ?ioa, ? ia i?eeeaae? ocaaaeueiaiiai ?ica’yceo Eacia?a
iieacaii yaii, ui aeeiai?ea Anana?oo a oeeo cia?aaeaiiyo nooo?ai
a?ae??ciy?oueny.

Iieacaii, ui noaa?eueia eiiiaeoeo?eaoe?y aioo??oi?o i?inoi??a
a?aeaoaa?oueny aeey iiaeaeae, a yeeo aoaeoeaiee iioaioe?ae ia? i?i?ioie
o i?inoi?? aioo??oi?o ianooaaieo oaeoi??a. Oea ocaaaeueith? ?acoeueoao
Ia?aee ( Maeda, 1986 ) ia aeia?eueio e?euee?noue aioo??oi?o i?inoi??a.

Aia?oa iieacaii, ui eiioi?ii? caoaeaeaiiy iao?eee aioo??oi?o i?inoi??a
aaaeooue naaa ye ianeai? neaey?i? iiey, ye? ?iciianthaeaeothoueny ia
oii? ciai?oiueiai i?inoi?o-/ano. A?aeiia?aei? /anoeiee iaea?aeaee iacao
a?aa?oaoe?eieo aeneoii?a, ? ?o a?aee?eooy iiaea noaoe aeieacii
?nioaaiiy aeiaeaoeiaeo aei???a.

Aia?oa aeeiiaii eaiii?/ia eaaiooaaiiy aaaaoiaei??ieo einiieia?/ieo
iiaeaeae c aeia?eueiith e?euee?noth aioo??oi?o i?inoi??a. Iaea?aeaia
aiane?aeie eaaiooaaiiy ??aiyiiy Oiea?a-aea Aiooa ia?
eaeia?iai/ii-eiaa?iaioiee aeaeyae. Oaeee i?aeo?ae ? ocaaaeueiaiiyi
i?ioeaaeo?e eaaiooaaiiy /ioe?eaei??ieo einiieia?/ieo iiaeaeae ( aeea.,
iai?eeeaae, Halliwell, Hawking, 1985).

Iieacaii, ui eaaioia? aiaeiae ?icaeyiooeo o aeena?oaoe?? aaaaoiaei??ieo
iioaa?iaieo eeane/ieo iiaeaeae oaeiae ? iioaa?iaieie, ? aeey an?o ?c ieo
iaea?aeaii iia? oi/i? ?ica’ycee ??aiyiue Oiea?a-aea Aiooa.

Aia?oa iiaoaeiaaii ?ica’ycee ??aiyiue Oiea?a-aea Aiooa, ui
caaeiaieueiythoue e?aeiaei oiiaai aaaaoiaei??ieo eaaioiaeo e?ioiaeo
i??. Aeeiiaii i?ioeaaeo?o o?aoeiiiai eaaiooaaiiy ia i?eeeaae?
aaaaoiaei??ieo iiaeaeae c aeia?eueiith e?euee?noth ??//i-ieineeo
aioo??oi?o i?inoi??a ? aia?oa iieacaii aeey oeeo iiaeaeae, ui niaeo?
/enea Anana?o?a, ia?iaeaeaieo ?c ii/aoeiaiai aaeooiiiai noaio, ia?
oaieiaee oa?aeoa?.

Aia?oa ?icaeyiooi eaaioiaa ia?iaeaeaiiy ( ooiiaethaaiiy )
aaaaoiaei??iiai Anana?oo ?c eeane/ii caai?iiaii? iaeano? ? iieacaii, ui
iiaeia i?ae?a?aoe ia?aiao?e iiaeae? oaeei /eiii, ui i?ney niiioaiiiai
ia?iaeaeaiiy ciai?oi?e i?ino?? cacia? iioeyoe?eiiai ?icoe?aiiy, a
aioo??oi? i?inoi?e noeneathoueny aei ieaie?anueeeo ianooaa?a.

I?aeoe/ia cia/aiiy iaea?aeaieo ?acoeueoao?a.

Iaea?aeai? ?acoeueoaoe iathoue ooiaeaiaioaeueia cia/aiiy, ai ?iaeyoue
cia/iee aianie o ?icaeoie iiaiai iai?yieo – eeane/ii? ? eaaioiai?
aaaaoiaei??ii? einiieiaii. Io?eiai? ?ica’ycee aeathoue iiaeeea?noue
aeine?aeeoe aeieeiaiiy ? aaiethoe?th Anana?oo c aeiaeaoeiaeie aei??aie
? iieacothoue, yeei /eiii aaaaoiaei??iee Anana?o iiaea noaoe aoaeoeaii
/ioe?eaei??iei, i?aeoaa?aeaeoth/e oei naiei i?eioeeiiao iiaeeea?noue
?nioaaiiy aeiaeaoeiaeo aei???a. Iniaeeaa i?aeoe/ia cia/aiiy ia?
caaaa/aiiy ?nioaaiiy iiaeo /anoeiie – a?aa?oaoe?eieo aeneoii?a,
ine?eueee a?aee?eooy oeeo /anoeiie noaei ae i?aeoaa?aeaeaiiyi ?nioaaiiy
aeiaeaoeiaeo aei???a.

Iniaenoee aianie caeiaoaa/a.

A ?iaioao [11, 12, 15, 16, 19, 24] caeiaoaa/ai io?eiaii iia? oi/i?
?ica’ycee eeane/ieo aaaaoiaei??ieo einiieia?/ieo iiaeaeae.

-iiaeae? ?c naiiae??th.

O ?iaio? [30] aaoi? iaea?aeaa oi?ioee, ui ca’ycothoue i?ae niaith
?ica’ycee o cia?aaeaiiyo A?aina-Ae?eea ? Aeiooaeia.

A ?iaio? [8] aaoi?ii anoaiiaeaii oiiae, ca eio?eo iiaeae?, ui
?icaeyaeathoueny, aeicaieythoue ?ica’ycee ?c noaoe/ieie aioo??oi?ie
i?inoi?aie. A noaooyo [25] – [28] aaoi? iieacaa, ui oe? noaoe/i?
?ica’ycee aoaeooue noaaieueieie, yeui aoaeoeaiee iioaioe?ae o
cia?aaeaii? Aeiooaeia ia? i?i?ioie, a iae? cao?aiiy a?ey i?i?ioi?a
aaaeooue naaa o ciai?oiueiio i?inoi?? ye ianeai? neaey?i? /anoeiee –
a?aa?oaoe?ei? aeneoiie.

A ?iaio? [28] aaoi? iieacaa, ui iiaeia iiaoaeoaaoe aaaaoiaei??i?
einiieiae/ii iiaeae?, a yeeo ciai?oi?e ( iao ) i?ino?? aaaea naaa ye
Anana?o O?iaeiaia, a aioo??oi? i?inoi?e ? noaa?eueii
eiiiaeoeo?eiaaieie.

A ?iaio? [1] aaoi?ii i?iaaaeaiii ?ic?aooiee ca i?ioeaaeo?ith
eaiii?/iiai eaaiooaaiiy aaaaoiaei??ieo einiieia?/ieo iiaeaeae. A ?iaioao
[2, 7, 12] aeena?oaioii io?eiaii iia? oi/i? ?ica’ycee eaaioiaiai
??aiyiiy Oiea?a-aea Aiooa.

Ai?iaaoe?y ?acoeueoao?a aeena?oaoe??.

Iniiai? ?acoeueoaoe aeine?aeaeaiue, aeeth/aieo a aeena?oaoe?th,
aeiiia?aeaeenue ia oaeeo eiioa?aioe?yo :

rz, 1994.

I?aeia?iaeia oeiea-nai?ia? ” Aaaaoiaei??ia a?aa?oaoe?y ? einiieiaiy “,
ss?ineaaeue, 20 – 26 /a?aiy 1994 ?.

I?aeia?iaeia iaoeiaa eiioa?aioe?y “Ano?io?ceea ? einiieiaiy i?ney
Aaiiaa”, i?enay/aia 90-??//th c aeiy ia?iaeaeaiiy A. A. Aaiiaa, Iaeana,
5 -10 aa?aniy 1994 ?.

VI i?aeia?iaeiee nai?ia? ” Eaaioiaa oai??y a?aa?oaoe?? “, i?enay/aia
iai’yo? aeaaeai?ea I. A. Ia?eiaa, Iineaa, 12 – 19 /a?aiy 1995 ?.

I?aeia?iaeia oeiea-nai?ia? ” Canaaee oai??? a?aa?oaoe?? ? einiieiaii “,
Iaeana, 4 -10 aa?aniy 1995 ?.

rz 1996.

?in?enueea a?aa?oaoe?eia eiioa?aioe?y “Oai?aoe/i? ? aenia?eiaioaeuei?
i?iaeaie a?aa?oaoe??”, Iiaai?iae, 24 – 30 /a?aiy 1996 ?.

8-th Marcel Grossmann meeting “On recent developments in Theoretical
and Experimental General Relativity, Gravitation and Relativistic Field
Theories”, Jerusalem, June 22 – 27, 1997.

International Workshop ” Modern Theories of Gravitation and Cosmology
“, Beer Sheva, June 29 – 30, 1997.

I?aeia?iaeia oeiea-nai?ia? ” I?iaeaie oai?aoe/ii? einiieiaii “,
Oeueyi?anuee, 1 – 7 aa?aniy 1997 ?.

I?aeia?iaeia eiioa?aioe?y c einiii?e?ioiceee ” Einiiii – 97″,
i?enay/aia 10 ?ieiaeiai iai’yo? ss. A. Caeueaeiae/a, Iineaa, 8 – 14
a?oaeiy 1997 ?.

International Seminar on Mathematical Cosmology, Potsdam, 30 March – 4
April, 1998.

?acoeueoaoe aeine?aeaeaiue aeiiia?aeaeenue oaeiae ia nai?ia?ao a
oi?aa?neoaoao i.Eaia?iaeaea (Aiae?y), i.O?aeao?aa (I?ia//eia),
i.Eiinoaioea (I?ia//eia), i.Iionaeaia (I?ia//eia), i.Aa?e?io (A?eueiee
oi?aa?neoao ? Oaoi?/iee oi?aa?neoao), a Aea?aeaaiiio ano?iiii?/iiio
?inoeooo? ?i. I.E.Ooa?iaa?aa (i.Iineaa), a ?inoeooo?
oai?aoe/ii? o?ceee ?i.I.I.Aiaiethaiaa (i.Ee?a).

Ioae?eaoe??.

Iniiai? ?acoeueoaoe iioae?eiaai? a 26 noaooyo a iaoeiaeo aeo?iaeao (c
eio?eo 12 noaooae ? naiino?eieie ioae?eaoe?yie aac ni?aaaoi??a), a 2
ca??eao iaoeiaeo i?aoeue ? a 2 i?ai?eioao.

No?oeoo?a ? ianya aeena?oaoe??.

Aeena?oaoe?y neeaaea?oueny c anooio, oanoe ?icae?e?a, aeniiae?a, i’yoe
aeiaeaoe?a ? nienea ae-ei?enoaieo aeaea?ae, ui aeeth/a? 383
iaeiaioaaiue. Iiaiee ianya aeena?oaoe?? neeaaea? 327 noi??iie, c yeeo
nienie e?oa?aoo?e caeia? 33 noi??iee ? aeiaeaoie – 45. A aeena?oaoe??
i?eaaaeaii 23 iaethiee.

INIIAIEE CI?NO ?IAIOE

O anooi? iaa?oioiaaii aeooaeuei?noue oaie aeena?oaoe?? ?
noi?ioeueiaaii oe?e? ?iaioe. Ina?oeaii iaea?eueo aaaeeea? i?iaeaie,
yeeie caeia?oueny aaaaoiaei??ia eeane/ia ? eaaioiaa einiieiaiy, ?
aeeiiaii iaeyae e?oa?aoo?e c oeeo ieoaiue. Noenei iiaeaii iniiai?
?acoeueoaoe ?iaioe ? aecia/aii i?noea aeine?aeaeaiue, ye?
?icaeyaeathoueny o aeena?oaoe??, na?aae ?ioeo ?ia?o.

caciaea niiioaiii? eiiiaeoeo?eaoei?

,
(1)

– aioo??oi? i?inoi?e. Iao?eea ia oe?e aaaaoinoaoiino? ia? aeae

, (2)

.

Ae?y aeey iiaeaeae, ui aeine?aeaeothoueny, ia? aeaeyae

, (3)

– ae?y iaoa??aeueieo (iaa?aaioaoe?eieo) iaeii??aeieo iieae.

)-aei??iiio i?inoi?? (iiiinoia?i?inoi??), yea iieno?oueny
eaa?aiaeiaiii

, (4)

– eiiiiiaioe iiiinoia?i?inoi?iai? iao?eee

. (5)

aecia/a?oueny oi?ioeith

, (6)

.

iiaea aooe aeiaaiiaeiciaaia a ??cieo eii?aeeiaoieo nenoaiao.
Iaea?eueo c?o/ieie aeyaeythoueny oae? aea? eii?aeeiaoi? nenoaie:

(7)

?

, (8)

,

. A oeeo nenoaiao iiiinoia?i?inoi?iaa iao?eea ia? aeaeyae

. (9)

A aeena?oaoe?? iieacaii, ui ia?oo eii?aeeiaoio nenoaio c?o/ii
aeei?enoiaoaaoe a cia?aaeaii? A?aina – Ae?eea, ine?eueee a oeueiio
cia?aaeaii? aeeiai?/iee ia’?i Anana?oo aecia/a?oueny ye

.
(10)

.

aeaeo

, (11)

. Iieacaii, ui ianooaai? oaeoi?e iathoue aeaeyae a?aeiia?aeii

(13)

i

, (14)

o ae?oaiio.

, ui, a?aeiia?aeii, caaeiaieueiythoue ??aiyiiyi

(15)

i

, (16)

, Anana?o aeey iaio oei?a ?ica’yceia iieno?oueny ocaaaeueiaiei
?ica’yceii Eacia?a:

(17)

.

. Aeey an?o oeeo aeiaaee?a i?eaaaeaii oi/i? ?ica’ycee ? iienaii
aeeiai?/io iiaaae?ieo ianooaaieo oaeoi??a.

-eii?aeeiao ? ??aiicia/iei. Io?eiai? aeey oe??? iiaeae? ?ica’ycee
?icaeaathoueny ia aeaa oeie:

, (18)

.

, (19)

.

.

):

, (20)

( aeiaaeie aaeeeeo aaiiao??e ) a?aeaoaa?oueny icio?iiicaoe?y
?icoe?aiiy

, (21)

.

).

):

, (22)

.

. A oeeo a?aie/ieo aeiaaeeao ?ica’ycee iiaiaeyoue naaa ye ocaaaeueiai?
?ica’ycee Eacia?a (18). Aaeee? aaiiao??? a?aeiia?aeathoue eeane/ii
caai?iiai?e aaee?aeia?e iaeano?.

). Oiae? iao?eeo i?inoi?o-“/ano” iiaeia caienaoe a oaeiio aeaeyae?:

. (23)

io?eio?ii

. (24)

. Oaeee ia’?eo, ca icia/aiiyi, ia? iacao aaee?aeiai? e?ioiai? ii?e.

Io?eiai? a oeueiio ?icae?e? ?ica’ycee iiaeooue neoaeeoe ye aeey
aea/aiiy iiaaae?iee aaaaoiaei??ieo iiaeaeae, oae ? aeey iieno aeeiai?ee
/ioe?eaei??ieo ai?cio?iiieo iiaeaeae.

-aei??ii? iiaeae?, yea iieno?oueny /enoi aaiiao?e/iith ae??th

. (25)

-aei??ia iao?eea (2), yea aecia/aia ia aaaaoinoaoiino? (1),
ocaaaeueiaia ia iaiaeii??aeiee aeiaaeie:

, (26)

.

-aei??ii? ae??

, (27)

, ae?th (27) iiaeia ia?aienaoe oaeei /eiii :

(28)

, ye /a?ac e?iaoe/io, oae ? /a?ac iioaioe?aeueio aia?a?th.

, oai??? oeio A?aina-Ae?eea iathoue aeaeyae oai??e a?aa?oaoe?? ?c
ci?iiith a /an? a?aa?oaoe?eiith “noaeith”. Iiee ui a aeiaeiiio ?c
aenia?eiaio?a aa??aoe?th a?aa?oaoe?eii? noaei? aeyaeoe ia aaeaeiny.
A?aoiaoth/? oe? caoaaaeaiiy, i?e?iaeiuei ia?aeoe aei ?ioiai
cia?aaeaiiy, aea an? neaey?i? iiey, ui aeieeathoue ca ?aooiie
aeiaeaoeiaeo aei???a, aoaeooue aoiaeeoe aei ae?? c ii?iaeueieie ciaeaie
e?iaoe/ieo /eai?a, ? aeeeaoiiia iiea ia aoaea c/aieaia c e?eaeciith.
Oaea cia?aaeaiiy ie aoaeaii iaceaaoe cia?aaeaiiyi Aeiooaeia, ? iao?eeo
ciai?oiueiai i?inoi?o naia o oeueiio cia?aaeaii? aoaeaii aaaaeaoe
o?ce/iith.

Ia?ao?ae a?ae cia?aaeaiiy A?aina-Ae?eea aei cia?aaeaiiy Aeiooaeia
a?aeaoaa?oueny ca aeiiiiiaith eiioi?iiiai ia?aoai?aiiy iao?eee:

,
(29)

,io?eia?ii

, (30)

-aei??iiai aaee?aeiaa i?inoi?o ?

(31)

(flat target space) ? naiiae??th, yea iieno?oueny iioaioe?aeii (31).

, aea “oeeueaeiaai?” aaee/eie a?aeiinyoueny aei cia?aaeaiiy Aeiooaeia.
Aeei?enoiaoth/e oe? oi?ioee, io?eio?ii, ui ocaaaeueiaiee ?ica’ycie
Eacia?a (18) o cia?aaeaii? Aeiooaeia iaaoaa? aeaeyaeo

, (32)

, oiaoi ciai?oi?e i?ino?? aaaea naaa ye cae/aeiee Anana?o O??aeiaia,
caiiaiaiee ?a/iaeiith c iaaeaei?noeei ??aiyiiyi noaio (ui aea?aaeaioii
i?i?iaeueiiio neaey?iiio iieth).

.

A /aoaa?oiio ?icae?e? aeine?aeaeo?oueny iaeia ?c iniiaieo i?iaeai
aaaaoiaei??ii? einiieia?? – i?iaeaia noaa?eueii? eiiiaeoeo?eaoe??
aioo??oi?o i?inoi??a. sseui aioo??oi? i?inoi?e ? eiiiaeoieie ? ?o
ianooaai? oaeoi?e iathoue ?ici??e ii?yaeeo ieaie?anueei? aeiaaeeie, oi
o oeueiio aeiaaeeo niinoa??aa?ia /anoeia Anana?oo ? aoaeoeaii
/ioe?eaei??iith. Oaeei /eiii iiaeia iiynieoe ianiinoa??aa?i?noue
aeiaeaoeiaeo aei???a. C ?ioiai aieo, aeiaeai c aenia?eiaio?a aein? ia
aeyaea aa??aoe?? ooiaeaiaioaeueieo o?ce/ieo noaeeo, iai?eeeaae
a?aa?oaoe?eii? noaei?, ioaea, aioo??oi? i?inoi?e ia aeaiee iiiaio /ano
iiaeii? aooe noaoe/ieie /e iaeaea noaoe/ieie.

Oiio a /aoaa?oiio ?icae?e? anoaiiaeaii oiiae, ca yeeo aeine?aeaeoaai?
aaaaoiaei??i? einiieia?/i? iiaeae? iiaeooue iaoe ?ica’ycee ?c noaoe/ieie
aioo??oi?ie i?inoi?aie. Anoaiiaeaii, iai?eeeaae, ui einiieia?/i?
iiaeae? a i?enooiino? i?i?iaeueiiai neaey?iiai iiey c a?aei?iiei a?ae
ioey iioaioe?aeii ia iathoue ?ica’yce?a ?c noaoe/ieie aioo??oi?ie
i?inoi?aie.

, oi aoaeoeaiee iioaioe?ae (31) iaaoaa? aeaeyaeo

. (33)

aea? iiaeeea?noue aeine?aeaeoaaoe ia o?eueee iiaeae? c ?aeaaeueiith
??aeeiith ??cieo oei?a, aea oaeiae a?aoiaoaaoe aaeooii? oeoeooaoe??
eaaioiaaieo iie?a, ui aeieeathoue caaaeyee eiiiaeoiino? aioo??oi?o
i?inoi??a (aoaeo Eaceie?a), a oaeiae iiiiiieuei? eiio?ao?aoe??.

.

ciai?oiueiai i?inoi?o-/ano:

, (34)

-aei??ia einiieia?/ia noaea.

Oaeei /eiii, eiioi?ii? caoaeaeaiiy iao?eee aioo??oi?o i?inoi??a
iiaiaeyoue naaa ye ianeai? neaey?i? iiey, ui ?iciianthaeaeothoueny ia
oii? ciai?oiueiai i?inoi?o-/ano. Ca aiaeia??th c aeneoiiaie o o?ceoe?
oaa?aeiai o?ea, ye? ? caoaeaeaiiyie aeaeo?iiii? i?aenenoaie e?enoaeo,
caoaeaeaiiy aioo??oi?o i?inoi??a iiaeia iacaaoe a?aa?oaoe?eieie
aeneoiiaie.

C o?ce/ii? oi/ee ci?o c?icoi?ei, ui aoaeoeaiee iioaioe?ae iiaeiai
caaeiaieueiyoe oaeei oiiaai:

,

, (35)

.

.

.

aeeiiothoueny.

-eiiiiiaioii? ?aeaaeueii? ??aeeie caeaaeeoue a?ae ianooaaiiai oaeoi?o
ciai?oiueiai i?inoi?o. A oeueiio aeiaaeeo eiiiiiaioe ?aeaaeueii?
??aeeie aea?ai? oaeei /eiii, ui aoaeoeaiee iioaioe?ae (33)
?icaeaa?oueny ia aea? /anoeie:

, (36)

? iane a?aa?oaoe?eieo aeneoii?a ni?aiaaeathoue c ae?acaie,
iaaaaeaiieie aeua aeey /enoi aaiiao?e/iiai aeiaaeeo. A oe?e iiaeae?
iiaaae?iea ianooaaiiai oaeoi?a ciai?oiueiai i?inoi?o iieno?oueny o
ioeueiaiio iaaeeaeaii? ( aac a?aooaaiiy caoaeaeaiue aioo??oi?o
i?inoi??a) oi?ioeith

, (37)

.

.

. Ie io?eio?ii ?aae?aoe?eii-aeii?iiaaiee Anana?o ia ii/aoeiaeo aoaiao
eiai aaiethoe?? ? Anana?o, caiiaiaiee ieeii, ia i?ci?o?o aoaiao.

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