Aei?i?iiao?ianueeee aea?aeaaiee oi?aa?neoao

Caneaanueeee Ieaenaiae? TH??eiae/

OAeE 539.12

Aaeooi oiiieia?/ii-ianeaieo iie?a ssiaa – I?eena

i?e ioeueia?e oa ne?i/aii?e oaiia?aoo??

01.04.02 – oai?aoe/ia o?ceea

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

nooiaiy eaiaeeaeaoa o?ceei-iaoaiaoe/ieo iaoe

Aei?i?iiao?ianuee – 1999

Aeena?oaoe??th ? ?oeiien.

?iaioa aeeiiaia ia eaoaae?? eaaioiai? iae?io?ceee

Aei?i?iiao?ianueeiai aea?aeaaiiai oi?aa?neoaoo.

Iaoeiaee ea??aiee aeieoi? o?ceei-iaoaiaoe/ieo iaoe

i?ioani? Neaeicoa Aieiaeeie? Aaneeueiae/,

caa?aeoaa/ eaoaae?e eaaioiai? iae?io?ceee,

Aei?i?iiao?ianueeee aea?aeaaiee oi?aa?neoao

Io?oe?ei? iiiiaioe aeieoi? o?ceei-iaoaiaoe/ieo iaoe

i?ioani? E??aa ?eey Aaeaioeiiae/,

i?ia?aeiee iaoeiaee ni?a?ia?oiee,

O?ceei-oaoi?/iee ?inoeooo

iecueeeo oaiia?aoo? (i.Oa?e?a)

aeieoi? o?ceei-iaoaiaoe/ieo iaoe

i?ioani? Ooo?e ?oneai Naiaiiae/,

i?ioani? eaoaae?e oai?ao?/ii? o?ceee,

Aei?i?iiao?ianueeee aea?aeaaiee oi?aa?neoao

I?ia?aeia onoaiiaa ?inoeooo oai?aoe/ii? o?ceee IAI

Oe?a?ie ?i. I.I.Aiaiethaiaa, i. Ee?a

Caoeno aeena?oaoe?? a?aeaoaeaoueny “ 22 ” aeiaoiy 1999?.
i “ 15 ” aiae. ia can?aeaii? niaoe?ae?ciaaii? a/aii? ?aaee Ae
08.051.02 ii caoenoo aeena?oaoe?e ia caeiaoooy a/aiiai nooiaiy
eaiaeeaeaoa o?ceei-iaoaiaoe/ieo iaoe i?e Aei?i?iiao?ianueeiio
aea?aeaaiiio oi?aa?neoao? ca aae?anith: 320625, i.Aei?i?iiao?ianuee,
i?ia. Iaoeiaee, 10, ei?i. 11, aoae. 301.

C aeena?oaoe??th iiaeia iciaeiieoenue o iaoeia?e a?ae?ioaoe?
Aei?i?iiao?ianueeiai aea?aeaaiiai oi?aa?neoaoo.

Aaoi?aoa?ao ?ic?neaiee “ 21 ” aa?aniy 1999?.

A/aiee nae?aoa?

niaoe?ae?ciaaii? a/aii? ?aaee i?ioani? Nie?eaeiiiaa ?.I.

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue oaie. Aea/aiiy aeanoeainoae iaaaaeaaeo eae?a?oaaeueieo
oai??e ? iaeiei c iniiaieo iai?yie?a no/anii? eaaioiai? oai??? iiey.
Aeine?aeaeaiiy aaeooio noaiaea?oii? iiaeae? a ??ciiiai?oieo
aeno?aiaeueieo ciai?oi?o oiiaao i?ecaaee aei aaaaoueio oe?eaaeo
?acoeueoao?a. Ia/eneaiiy aoaeoeaiiai iioaioe?aeo aethiiieo iie?a o
ciai?oiueiio eieuei?iaiio iaai?oiiio iie? iieacaee, ui i?i?ioio aia?a??
a?aeiia?aea? iaioeueiaa cia/aiiy iaai?oiiai iiey. Iaeiae, iiaeaeueoa
aeine?aeaeaiiy aeiaaei, ui niaeo? aethii?a i?noeoue oao?iiio iiaeo —
iiaeo c a?ae’?iiei eaaae?aoii aia?a??. Oea i?ecaiaeeoue aei iiyae
oyaiiai aianeo aei aoaeoeaiiai iioaioe?aeo ?, oaeei /eiii, niiioaiii
iaiaai?/aiee noai ? ianoaa?eueiei. Iiooe iiaeeeaeo cania?a noaa?e?caoe??
aaeooio noaiaea?oii? iiaeae? i?eca?a aei a?aee?eooy yaeua eiiaeainaoe??
eae?a?oaaeueieo iie?a. Oa?aeoa?ieie iniaeeainoyie oeueiai oaiiiaio ?
oi?ioaaiiy ia??iaee/ii? no?oeoo?e o aaeooi? caaaeyee caoaeaeaiith
oao?iiii? iiaee a ?ioaineaieo iieyo aai aonoiio na?aaeiaeu?, a oaeiae
i?enooi?noue neaey?iiai iiey, yea noaa?e?co? eiio?ao?aoe?th. Iaoai?ci
eiiaeainaoe?? a oe?eiio iiae?aiee aei oaeiai, ui ae?? a oai???
iaaei?ia?aeiino?, aea iioiaeaeaiiy eiiieaenieo iiae o niaeo?? noooaai
a?ae??ciy?oueny. Aeine?aeaeaiiy eae?a?oaaeueieo iie?a o aeaio
i?inoi?iaeo aei??ao aeiaaee, ui a oeueiio aeiaaeeo oaeiae i?enooiy
ianoaa?eueia iiaea niaeo?o, yea iiaea i?eaiaeeoe aei eiiaeainaoe??
aethiiieo iie?a.

Oai??? eae?a?oaaeueieo iie?a o (2+1)-aei??iiio i?inoi??-/an?
i?eaa?oathoue aei naaa aaeeeo oaaao a inoaii? i?aoi?a aeanyoe??//y. Oeae
?ioa?an iiaeia iiynieoe aeae?eueeiia i?e/eiaie. Ii-ia?oa, aeaiaei??i?
oai??? iathoue oae? aeanoeaino?, ui a cia/i?e i??? a?ae??ciythoue ?o
a?ae iiaeaeae o cae/iiio o?eaei??iiio na?o?. I?eeeaaeii iiaea neoaeeoe
iiaeeea?noue iaaeaoe eae?a?oaaeueiiio iieth iano, oae caaio oiiieia?/io
iano *a?ia–Naeiiina, ia ii?oooth/e eae?a?oaaeueii? ?iaa??aioiino?
oai???. Oaeoe/ii, yeui ia aaanoe cao?aai/iee ianiaee /eai, oi a?i aoaea
caaia?iaaiee o aoaeoeaiiio eaa?aiae?ai? ca ?aooiie oa?i?iiieo iaoeaaeo
iii?aaie. Ii-ae?oaa, i?e aenie?e oaiia?aoo?? iieueia? oai??? o
(3+1)-aei??iiio i?inoi?? aoaeoeaii iiaiaeyoue naaa, ye oai??? o o?ueio
aaee?aeiaeo aei??ao. Ii-o?ao?, iecueeiaei??i? iiaeae? oai??? iiey
aeiioneathoue ?nioaaiiy /anoeiie, ui i?aeii?yaeeiaothoueny aiiiaeuei?e
noaoenoeoe? ? iathoue ae??aiee ca?yae, oa oni?oii canoiniaothoueny aei
aea/aiiy yaeu oai??? eiiaeainiaaiiai noaio — eaaioiaiai aoaeoo Oieea,
aenieioaiia?aoo?ii? iaaei?ia?aeiino?, — ui iathoue nooo?ai ieaia?io
i?e?iaeo.

Oaeei /eiii, aeine?aeaeaiiy aeaiaei??ieo oiiieia?/ii-ianeaieo iie?a
ssiaa–I?eena caeaoi? aeaoe a?aeiia?ae? ia ieceo aaaeeeaeo ieoaiue, ui
noiyoue o oeaio?? no/anii? oai??? eae?a?oaaeueieo aca?iiae?e.

Iaoa ?iaioe. Iaoith i?iaaaeaieo aeine?aeaeaiue aoei anoaiiaeaiiy aeanoe-
ainoae aaeooio iaaaaeaaeo eae?a?oaaeueieo iie?a c /a?i-naeiii?anueeith
ianith o aeaio i?inoi?iaeo aei??ao i?e ioeueia?e oa ne?i/aii?e
oaiia?aoo??. Aieiaia oaaaa i?eae?eyeany ieoaiith i?i iiaeeea?noue
aaia?aoe?? iao?ea?aeueieo iieueiaeo aaeooiieo eiio?ao?aoe?e, ui
aeieeathoue caaaeyee i?enooiino? iane aethii?a, a oaeiae c’ynoaaiith
aieeaa ne?i/aiii? oaiia?aoo?e ia iiaaae?ieo oa aeanoeaino? oaeeo
no?oeoo?.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie. Aeine?aeaeaiiy,
?acoeueoaoe yeeo neeaaeathoue aeena?oaoe?th, i?iaiaeeeeny o
a?aeiia?aeiino? c ieaiii iaoeiaeo ?ia?o eaoaae?e eaaioiai? iae?io?ceee,
oaiaoe/ieie ieaiaie iaoeiai-aeine?aeieo ?ia?o, ui i?iaiaeyoueny ca
i?ia?aiaie ooiaeaiaioaeueieo aeine?aeaeaiue I?iina?oe oa I?iiaoee
Oe?a?ie: 2.5.1/67 “Aoaeoeai? iae?i?ei? aca?iiae?? eae?a?oaaeueieo iie?a
o aeno?aiaeueieo ciai?oi?o oiiaao”, ? 161-96  “Aeine?aeaeaiiy
eae?a?iai/ieo oai??e o aeno?aiaeueieo iae?ioiiaao”, ? 09-98-98
 “Aeine?aeaeaiiy ooiaeaiaioaeueieo i?ioean?a o aeno?aiaeueieo ciai?oi?o
oiiaao iaoiaeaie eaaioiai? oai??? iiey”, ? 42-94  “Oaiiiaiieia?y
noaiaea?oii? iiaeae? ooiaeaiaioaeueieo aca?iiae?e o aeno?aiaeueieo
ciai?oi?o oiiaao”.

Iaoeiaa iiaecia iaea?aeaieo ?acoeueoao?a. Iaoeiaa iiaecia i?iaaaeaii?
?iaioe aecia/a?oueny ?acoeueoaoaie, ui iaea?aeai? aia?oa, c yeeo
iaeaaaeeea?oeie ? oae?:

I?iaaaeaii anaa?/iee aiae?c aaeooio oai??? iie?a ssiaa–I?eena c
/a?i-naeiii?anueeith ianith i?e ioeueia?e oa ne?i/aii?e oaiia?aoo??.

Aeiaaaeaii, ui iayai?noue /a?i-naeiii?anueei? iane m eae?a?oaaeueiiai
iiey i?ecaiaeeoue aei iiaeeeaino? noaa?e?caoe?? iaiaai?/aiiai aaeooiiiai
noaio; iaeiiiaoeaaee aoaeoeaiee iioaioe?ae aethiiieo iie?a ia? i?i?ioi
i?e H ( 0 aeey aoaeue-yeiai cia/aiiy m; ?nio? iaeanoue cia/aiue iane,
aeey yeeo cia/aiiy Veff a i?i?ioi? ? ae?eniei.

Ciaeaeaii ? aeine?aeaeaii iiaee iaoai?ci ooai?aiiy aaeooiiiai
eiiaeainaoo iaaaaeaaeo eae?a?oaaeueieo iie?a, ia iia’ycaiee c
aaiethoe??th oao?iiii? iiaee. Oeae iaoai?ci ae?? aeeeth/ii caaaeyee
i?enooiino? /a?i-naeiii?anueei? iane a iaai?oieo iieyo ieae/a ii?iao
ianoaa?eueiino? niaeo?o eae?a?o- aaeueieo iie?a ye i?e ioeueia?e, oae ?
i?e ne?i/aii?e oaiia?aoo??.

Ciaeaeaii iiaee oei ia??iaee/ii? no?oeoo?e aaeooio iaaaaeaai? eae?a?o-
aaeueii? oai???, ui ooai?th?oueny eiiaeainaoii ca?yaeaeaieo aethiiieo
iie?a. Oey eiio?ao?aoe?y ? ?ica’yceii ??aiyiue ?ooo, ui io?eiaiee
ia?oo?aaoeaiei iaoiaeii o eean? noaoe?iia?ieo ooieoe?e. Ia a?aei?io a?ae
iaaei?ia?aeiino? oa noaiaea?oii? iiaeae? o aaeooi? aaia?o?oueny ii?yae c
iaai?oiei oaeiae ? ia??iaee/ia aeaeo?e/ia iiea. Aeiaaaeaii iiaeeea?noue
niiioaiii? aaia?aoe?? aaeooiii? no?oeoo?e.

Iaea?aeaii oi/iee ?ica’ycie iae?i?eieo ??aiyiue ?ooo aeey aethiiieo
iie?a, ui aeieeaathoue c aoaeoeaiiai eaa?aiae?aio, yeee i?noeoue aianie
oaiia?aoo?ii? iane aeey eiiiiiaioe iioaioe?aea A0. Naia a?aooaaiiy
oeueiai aianeo ?iaeoue iiaeeeaei ?nioaaiiy ?ica’yceo, ui iieno? aeo?iao
iieueiao eiio?ao?aoe?th ?c ne?i/aiiith aia?a??th.

Anoaiiaeaii, ui, eiee ianooaa oaiia?aoo?e T ia ia?aaeuo? m, aeo?iaa
eiio?ao?aoe?y a?aeiia?aea? /anoeiei-iiae?aiei caoaeaeaiiyi c iiceoeaiith
aia?a??th iaae ia??iaee/iei aaeooiiei eiiaeainaoii. I?e aenie?e
oaiia?aoo?? aaeooi ianeaieo eae?a?oaaeueieo iie?a yaey? niaie nenoaio
?cieueiaaieo aeo??a c a?ae’?iiith aia?a??th, ui ? ?acoeueoaoii
aaiethoe?? ??aoee, noi?iiaaii? i?e T = 0.

I?aeoe/ia cia/aiiy iaea?aeaieo ?acoeueoao?a. I?aeoe/ia cia/aiiy ?iaioe
aecia/a?oueny a ia?oo /a?ao iiaeeea?noth canoinoaaiiy iaea?aeaieo
?acoeueoao?a a aeae?eueeio iai?yieao. Aeine?aeaeaiiy iieacaee, ui
i?enooi?noue oiiieia?/ii? iane i?ecaiaeeoue aei iiyae ii?iao aeieeiaiiy
oao?iiii? iiaee a niaeo?? aethii?a ? aaaea aei iiaeeeaino? noaa?e?caoe??
iaiaai?/aiiai aaeooio. Aeiaeaeaiee iaoai?ci aaia?aoe?? aaeooiiiai
eiiaeainaoo oa i?iaaaeaiee aiae?c no?oeoo?e aaeooio iinyoue caaaeueiee
oa?aeoa? ? iiaeooue aooe iioe?ai? ia aeineoue oe?ieee eean iiaeaeae.
Cie?aia, iiaeeeai ?o canoinoaaiiy o aeiaaeeo, eiee /a?i-naeiii?anueea
iana aaia?o?oueny caaaeyee ?ioaa?oaaiith ii oa?i?iiieo iieyo ia
iaeiiiaoeaaiio ??ai?. Iiaeia i/?eoaaoe, ui aeine?aeaeaiee iaoai?ci
i?eaaaea aei oi?ioaaiiy aaeooiieo no?oeoo? oaeiae o ??ciiiai?oieo
ciai?oi?o oiiaao: aeniea aonoeia, ?ioaineai? iiey. Oea
i?aeoaa?aeaeo?oueny i?iaaaeaiei aiae?cii aeiaaeeo ne?i/aiii?
oaiia?aoo?e. Nooo?aei ?acoeueoaoii ? anoaiiaeaiiy aaaeeeai? ?ie?, ui
a?ae?a?a? caaaeyee no?oeoo?? /eaia *a?ia–Naeiiina iioaioe?ae A0. Oea
aeiaiaeeoue iaiao?aei?noue a?aooaaiiy a?aeiia?aeiiai aianeo i?e
iiaoaeia? aoaeoeaieo eaa?aiae?ai?a eae?a?oaaeueieo iie?a.

sse a?aeiii, /a?i-naeiii?anuee? oai??? ? ei?eniei ?ino?oiaioii aeey
aeine?aeaeaiue o o?ceoe? eiiaeainiaaiiai noaio. Oiio iaea?aeai?
?acoeueoaoe iiaeooue ciaeoe canoinoaaiiy o aaeineiiaeaii? ?nioth/eo
iiaeaeae eaaioiaiai aoaeoo Oieea, aenieioaiia?aoo?ii? iaaei?ia?aeiino?.
E??i oiai, ine?eueee oai??? iiey a 3-aei??iiio aaee?aeiaiio i?inoi??
aoaeoeaii aea?aaeaioi? a?iia?aeiei oai??yi o (3+1)-aei??iiio na?o? i?e
aenie?e oaiia?aoo??, aea/ai? aeanoeaino? aaeooio iaaaaeaaeo iie?a ?
e?ieii ia oeyoo aei i?iyniaiiy aeanoeainoae aaeooio noaiaea?oii?
iiaeae?.

Iniaenoee aianie caeiaoaa/a. Iniiai? ?acoeueoaoe oa aeniiaee
aeena?oaoe?? io?eiai? iniaenoi aaoi?ii. Iinoaiiaea caaea/?, aecia/aiiy
iai?yie?a aeine?aeaeaiue oa iaaiai?aiiy iaea?aeaieo ?acoeueoao?a
i?iaiaeeeeny ?acii ?c iaoeiaei ea??aieeii aeieoi?ii o?c.-iao. iaoe
i?ioani?ii Neaeicoaii A.A. Ni?aaaoi? ioae?eaoe?e A?eainueeee N.I. a?aa
o/anoue o i?iaaaeaii? ia/eneaiue oa iaaiai?aii? ?acoeueoao?a
aeine?aeaeaiue.

Ai?iaaoeiy ?iaioe. Iniiaii ?acoeueoaoe aeena?oaoei? aeiiiaiaeaeeny e
iaaiai?thaaeeny ia oaeeo eiioa?aioe?yo: I?aeia?iaeia eiioa?aioe?y
“I?iaeaie oai?aoe/ii? oa iaoaiaoe/ii? o?ceee”, 1994?., Aeoaia, ?in?y;
Anaoe?a?inueea iaoeiai-i?aeoe/ia eiioa?aioe?y “Ethaeeia ? einiin”,
naeoe?y A?aa?oaoe?y ? ooiaeaiaioaeueia o?ceea, 1999?.,
Aei?i?iiao?ianuee; iiaenoieiaeo iaoeiaeo eiioa?aioeiyo
Aeiii?iiao?ianueeiai aea?aeoiiaa?neoaoo, Aeiii?iiao?ianuee,
1994–1998?.?.; naiiia?ao eaoaae?e eaaioiai? iae?io?ceee
Aeiii?iiao?ianueeiai aea?aeoiiaa?neoaoo, Aeiii?iiao?ianuee,
1993–1999?.?.

Iniiaii iieiaeaiiy aeena?oaoei? iioae?eiaaii o noaooyo [1–6] oa
ca??ieeo iaoa??ae?a aeiiia?aeae iaoeiai? eiioa?aioe?? [7].

No?oeoo?a oa ianya aeena?oaoe??. Aeena?oaoe?y neeaaea?oueny c? anooio,
/ioe?ueio ?icae?e?a, caeeth/aiiy, aeaio aeiaeaoe?a ? nieneo oeeoiaaii?
e?oa?aoo?e c 91 iaeiaioaaiiy ia 9 noi??ieao. Aeena?oaoe?y i?noeoue 1
oaaeeoeth, 5 ?enoie?a, ?? iiai?e ianya noaiiaeoue 117 noi??iie.

CIINO ?IAIOE

O anooi? ia??oioiaaii aeooaeuei?noue ia?aii? oaie aeine?aeaeaiue,
noi?ioeuei- aaii iaoo ?iaioe, aeacai? iaoeiaa iiaecia ? i?aeoe/ia
cia/ou?noue iaea?aeaieo ?acoeueoao?a, iaaaaeaii a?aeiiino? i?i no?oeoo?o
?iaioe, ?? ai?iaaoe?th oa iniaenoee aianie aaoi?a, eiiniaeoeaii
aeeeaaeaii ci?no aeena?oaoe??.

O ia?oiio ?icae?e?, yeee ia? iaeyaeiaee oa?aeoa?, ?ice?eaa?oueny
no/aniee noai iaoeiai? i?iaeaie, ui aeine?aeaeo?oueny, i?iaiae?ciaaii
?acoeueoaoe, io?eiai? a ?iaioao ?ioeo aaoi??a. Aeeeaaeaii iniaeeaino?
eae?a?oaaeueieo oai??e o (2+1)-aei??iiio i?inoi??, i?e/eie, ui ?iaeyoue
?o aea/aiiy iaiao?aeiei. Cie?aia, i?iaiae?ciaaii iiaeeea?noue aaaaeaiiy
oiiieia?/ii? iane eae?a?oaaeueiiai iiey, ca’ycie aeaiaei??ieo iiaeaeae c
oa?iaeueiith oai???th iiey o o?ueio aei??ao, ?o canoinoaaiiy aeey iieno
ieaia?ieo ca nai?th i?e?iaeith aoaeo?a o oai??? eiiaeainiaaiiai noaio.
I?iaaaeaii iaeyae iiooe?a iniiaiiai noaio iaaaaeaaeo iie?a, cie?aia
iayaiino? ianoaa?eueii? iiaee a aethiiiiio niaeo?? a iaai?oiiio iie? oa
iiaeeeaino? ooai?aiiy aaeooiiiai eiiaeainaoo eae?a?oaaeueieo iie?a.
Oaeei /eiii noi?ioeueiaaii i?aenoaae oa aeo?aei? aeai? aeey ?ic?iaee
oaie, ia??oioiaaii aeiaaaeaii iaiao?aei?noue i?iaaaeaiiy aeine?aeaeaiiy.

Ae?oaee ?icae?e ?iaioe i?enay/aii ia/eneaiith aoaeoeaiiai iioaioe?aeo
aethiiieo iie?a o oiiiaiio iaai?oiiio iie? aaaeaaa oeia a i?enooiino?
/a?i-naeiii?anueei? iane oa, ia iniia? io?eiaiiai ae?aco aeey Veff,
c’ynoaaiith ieoaiiy i?i iiaeeea?noue noaa?e?caoe?? iiey?eciaaiiai
iaai?oiei iieai aaeooio iaaaaeaai? eae?a?oaaeueii? oai???.

?icaeyaea?oueny eaa?aiae?ai aeaiaei??ii? SU(2)-aethiaeeiai?ee c
/a?i-naeiii?aneith ianith a aaee?aeia?e iao?eoe?:

(1)

; g — eiinoaioa aca?iiae??; m — /a?i-naeiii?anueea iana. Aeey
ia/eneaiiy iaeiiiaoeaaiai aianeo a aia?a?th aaeooia aeinoaoiuei
e?iaa?eciaaieo ??aiyiue ?ooo aeey iie?a aethii?a oa aeoo?a, ye? a
eae?a?iaoe? Oaeiiaia ( = 1 iathoue oaeee aeaeyae:

, (2)

, (3)

.

??aiyiiy ?ooo (2) aeey aethiiieo iie?a iiaeia caienaoe oae:

, (4)

aea (( — iao?eoe? aaia?aoi??a a?oie SU(2) o i?e?aeiaiiio (o?eaei??iiio)
i?aaenoaaeaii?; W = (W1, W2, W3). Niaeo? caoaeaeaiue eae?a?oaaeueiiai
iiey, ui aeieeaa? c oeueiai ??aiyiiy, ia? aeaeyae:

, (5)

. Iayai?noue ianoaa?eueii? iiaee aaaea aei iiyae oyaii? /anoeie
aoaeoeaiiai aethiiiiai iioaioe?aeo ? aeaco? ia ianoaa?euei?noue
iaiaai?/aiiai aaeooio.

Canoiniaoth/e iaoiae i?aenoiiaoaaiiy niaeo?o, io?eio?ii oaeee ae?ac aeey
iaeiiiaoeaai? iii?aaee aei aonoeie aia?a?? aaeooio:

,

. (7)

-ooieoe?? ??iaia ia a?ae’?ii? cia/aiiy s. Ia/eneaiiy aianeo aeooiaeo
iie?a i?iaiaeeoueny aiaeia?/ii ? aea? oaeee ae?ac:

. (8)

Iiaiee ?aii?iae?ciaaiee iaeiiiaoeaaee aoaeoeaiee iioaioe?ae aethiiiiai
iiey ia? aeaeyae:

(9)

.

Cacia/eii, ui oao?iiia iiaea niaeo?o aea? aianie ye aei oyaii?, oae ?
aei ae?enii? /anoeie Veff. Oeae ae?ac aea? iiaeeea?noue aea/aiiy
aeanoeainoae aaeooio i?e ??cieo cia/aiiyo /a?i-naeiii?anueei? iane oa
iaai?oiiai iiey.

Ia?aae on?i, yeui iieeanoe m = 0, oi (9) ia?aoai?th?oueny ia

, (10)

oa aeyaeee oaeo iiaaae?ieo iaiaai?/aiino? a caeaaeiino? a?ae iane m.
?c ca?eueoaiiyi ( aaeooiia na?aaei? iiey h iiiioiiii c?inoa?, a ImVeff
ciaioo?oueny. Eiee cia/aiiy iane ia?aaeuo? ( ( 0.565, aaeooiia iaai?oia
iiea ni?aiaaea? c ii?iaiaei hmin = h0, ? oyaia /anoeia aonoeie aia?a?? o
i?i?ioi? a?aenooiy. Aia?a?y iaiaai?/aiiai noaio ye ooieoe?y iane ia?
i?i?ioi i?e ( = 0.706 ? eaaeeoue aeua ioey i?e ( > 0.935. I?e
a?eueoeo m oeae noai noa? eaac?noaa?eueiei, aea iiiiaeaiiy neiao??? ia
a?aeaoaa?oueny, oiio ui i?e ( ( 0.718 o aoaeoeaiiio iioaioe?ae?
c’yaey?oueny eieaeueiee i?i?ioi o neaaeeo iieyo h ( 0.1 h0. Oeae iiaee
i?i?ioi ? noaa?eueiei, ? cia/aiiy aia?a?? o iueiio caaaeaee a?ae’?iia.
?nio? e?eoe/ia cia/aiiy (c ( 0.934, i?e yeiio aeiaaeueiee i?i?ioi
iioaioe?aea ci?ith? nai? iieiaeaiiy, ? aaeooiia iiea Hmin caeeoa?oueny
a?aei?iiei a?ae ioey i?e aoaeue-ye?e ian?. Oaeei /eiii, i?enooi?noue o
eaa?aiae?ai? /a?i-naeiii?anei? iane i?e iaaieo ?? cia/aiiyo noaa?e?co?
iaiaai?/ai?noue aaeooia aethiiiiai iiey. A oeueiio iieyaa? i?eioeeiiaa
a?aei?ii?noue a?ae aeiaaeeo aacianiaeo eae?a?oaaeueieo iie?a.

O o?aoueiio ?icae?e? aea/a?oueny iiaeeea?noue oi?ioaaiiy iao?ea?aeueii?
no?oeoo?e aaeooio oiiieia?/ii-ianeaieo iie?a ssiaa – I?eena. Iaoiae
aeine?aeaeaiiy ? aiaeia?/iei iaoiaeo, ui aoa ?icaeiooee Aa?eeiniaei o
oai??? iaaei?ia?aeiino? II ?iaeo. Caieoaii ??aiyiiy ?ooo aeey aethiiieo
iie?a o i?inoi?? I?ieianueeiai a ca?yaeiaiio aacen?:

(11)

, (12)

(13)

ia ia? noaoe/ieo ??oaiue. Oea iia’ycaia c oei, ui /a?i-naeiii?anueeee
/eai ci?oo? aeaeo?e/i? ? iaai?oi? eiiiiiaioe F(( ? i?eaiaeeoue aei
aaia?aoe?? aeaeo?e/iiai iiey. Oiio ie iioe?th?ii eean ooieoe?e, ui
?icaeyaeathoueny, ? ciaoiaeeii noaoe?iia?iee ?ica’ycie:

, (14)

, ? b( = (0, 1, i) — aeaniee aaeoi? iia?aoi?a ni?io. Ie aa/eii, ui
noaoe?iia?i? ?ica’ycee ?niothoue a iieyo H < H0 = m2/4g; a neeuei?oeo iieyo aaeooi oai??? cao?aiue ? ianoaa?eueiei. Ie iaaiai?th?ii a oe?e ?iaio? iiaee oei no?oeoo?e, ui ooai?th?oueny i?e H < H0 caaaeyee i?enooiino? oiiieia?/ii? iane. Eiee m ? iaeith, iae?i?ei?noue nenoaie iie?a oaae iaea ? iiaea aooe a?aoiaaia ia?oo?aaoeaieie iaoiaeaie. I?aaenoaaeii ?ica'ycie (11) a iieyo aeecueeeo aei e?eoe/iiai o aeaeyae? e?i?eii? eiia?iaoe?? (14) c ??cieie k: . (15) , , (16) , : . (17) Ciai?oia aeaea?aei eiiiaino? /a?i-naeiii?anueeee ca?yae, ? ie iaea?aeo?ii oae? ae?ace aeey iie?a, ui aaia?othoueny a nenoai?: , (18) , (19) , (20) , (21) ui ? iane?aeeii iae?i?eiino? nenoaie iie?a. Ai?iaaaeaeoth/e aac?ici??iee ia?aiao? , (22) ui oa?aeoa?eco? oi?io ??aoee, iiaeia io?eiaoe ae?ac aeey na?aaeiueiai aethiiiiai eiiaeainaoo . (23) ? ia caeaaeaoue a?ae /ano. Aonoeia aia?a?? eiio?ao?aoe?? aecia/a?oueny oi?ioeith . (24) Iaai?oia ?iaeoeoe?y — na?aaei? cia/aiiy i?e?ineii?/iiai iiey F12 : . (25) , ? nenoaia iie?a ? iaaeeneiaoeaiith. Ooo iiaeia iiaa/eoe oi?iaeueio aiaeia?th c aoaeoii Oieea. Iiaiee ca?yae aaeooio aei??aith? ioeth, aea eieaeueii eiaeia a?/ei ??aoee ia? iiceoeaii ca?yaeaeaia yae?i, ioi/aia ca?yaeii i?ioeeaaeiiai ciaeo. Oaeei /eiii, aaeooi iaaaaeaaeo oiiieia?/ii-ianeaieo iie?a ssiaa–I?eena i?aaenoaaeaiee ia??iaee/iith no?oeoo?ith, ui noi?iiaaia aethiiiei eiiaeainaoii ? ?aae?co?oueny aeeeth/ii caaaeyee i?enooiino? /a?i-naeiii?anueei? iane. Aaaeeeaeie iniaeeainoyie eiio?ao?aoe?? ? aaia?aoe?y aeaeo?e/iiai iiey oa iiaeeea?noue ?? niiioaiiiai ooai?aiiy. O /aoaa?oiio ?icae?e? i?iaaaeaii aeine?aeaeaiiy iiaaae?iee no?oeoo?e aaeooio eae?a?oaaeueieo iie?a i?ae aieeaii ne?i/aiii? oaiia?aoo?e. sse aeia?a aiae?c ooai?aiiy aethiiiiai eiiaeainaoo i?e ioeueia?e oaiia?aoo??, ia a?aei?io a?ae aeeeth/ii iaai?oii? ??aoee oai??? iaaei?ia?aeiino?, nooo?ao ?ieue a iaoai?ci? aaia?aoe?? a?ae?a?a? eiiiiiaioa iioaioe?aeo A0 . Oiio iaiao?aeii a?aoiaoaaoe aeaaa?anueeo iano aeey io?eiaiiy naiiocaiaeaeaieo ?acoeueoao?a. Aoaeoeaiee eaa?aiae?ai, ui iieno? iiaeaeue, ? oaeei: . (26) Ia/eneaiiy eiiiiiaioe I00 iiey?ecaoe?eiiai iia?aoi?a aethii?a aaaea aei ae?aco: (27) : . (28) ; cacia/eii, ui ?c ca?eueoaiiyi oaiia?aoo?e M2 ( g2T. Aaee/eia aethiiiiai eiiaeainaoo aecia/a?oueny oi?ioeith . (29) ( T, ? ia?oo?aaoeaiee iaoiae noa? iaaaeaeaaoiei. Aeey aecia/aiiy aaeooiiiai noaio a oeueiio aeiaaeeo iaiao?aeii i?iaiae?coaaoe iae?i?ei? ??aiyiiy ?ooo, ui aeo?eathoue c eaa?aiae?aio (26). ??aiyiiy ?ooo aeey oiiieia?/ii-ianeaieo aethiiieo iie?a, ui a?aoiao? oaeiae oaiia?aoo?io iano eiiiiiaioe iioaioe?aea A0, ia? aeaeyae: , (30) aea I00 aecia/a?oueny i?ia?aeiei /eaiii (27). Aeey oiai, uia ciaeoe oi/iee ?ica'ycie oeeo ??aiyiue, ai?iaaaeeii oaeee aicaoe aeey eae?a?oaaeueieo iioaioe?ae?a: . (31) . Iiaeaeueoa ni?iuaiiy a?aeaoaa?oueny, yeui iaiaaeeoeny aen?aeueii-neiao?e/ieie noaoe/ieie eiio?ao?aoe?yie,(i = (i (r), oa iieeanoe A (r) = = 1/gr. Oiae? aicaoe (31) iieno? nenoaio iie?a, ui oi?iothoue aeoi? o eii?aeeiaoiiio oa aioo??oiueiio i?inoi?ao. ??aiyiiy ?ooo (30) ni?iuothoueny aei e?i?eii? nenoaie (32) ?ica'ycie yei? ae?aaea?oueny /a?ac iiae?o?eiaai? ooieoe?? Aannaey: , (33) aea ciia c'yaey?oueny aoaeoeaia iana M; a, c — eiinoaioe ?ioaa?oaaiiy. Io?eiai? ae?ace aeey eae?a?oaaeueieo iioaioe?ae?a (34) aeiiiaioe?aeueii niaaea? ia i?inoi?ia?e iane?i/aiiino? aei /enoi? eae?a?iaee. A?aeiia?aeii, aeaeo?e/ia oa iaai?oia iiey , (35) (36) ? ei?ioeiae?th/eie; ?ici?? aeo?iai? eiio?ao?aoe?? aecia/a?oueny aoaeoeaiei ianiaei ia?aiao?ii M. Iaai?oiee iio?e ne??cue 2-i?ino?? aei??aith? . (37) a oeaio?? aeoi?o. ?iciiae?eaiee ca?yae aecia/a?oueny oi?ioeith (38) ? oiio a oe?eiio io?eiaia eiio?ao?aoe?y iie?a ? iaeo?aeueiith. Aiae?c ae?aco aeey iiaii? aia?a?? nenoaie (39) aeiaiaeeoue, ui ca aeiiiiiaith iaeaaeiiai aeai?o eiinoaio a, c iiaeia iicaaaeoeny neiaoey?iino? a ?ioaa?aiae? i?e r = 0, . (40) Oiae? iiaia aia?a?y aeo?iai? eiio?ao?aoe?? ? ne?i/aiiith: . (41) = 0. sse aeaeii c (41), ciae aia?a?? aeoi?o aecia/a?oueny ni?aa?aeiioaiiyi i?ae /a?i-naeiii?anueeith oa aeaaa?anueeith ianaie. Eiee m > (, aia?a?y
? iiceoeaiith, ? io?eiaiee ?ica’ycie iieno? aeaiaei??iee oaiia?aoo?iee
nie?oii. Iniiaiei noaiii oai??? ? ia??iaee/iee aethiiiee eiiaeainao, a
aeoi? a?aeiia?aea? /anoeiei-iiae?aiei caoaeaeaiiyi iaae ??aoeiaei
aaeooiii. I?e aenie?e oaiia?aoo??, ( > m, neooaoe?y i?eioeeiiai ?ioa.
Eiio?ao?aoe?y ia? a?ae’?iio aia?a?th oa, ye iane?aeie, a?aeiia?aea?
iniiaiiio noaio. Oeae aaeooi iiaeii ?icaeyaeaoe ye ?acoeueoao aaiethoe??
ia??iaee/ii? no?oeoo?e, ui noi?iiaaia i?e T = 0. Iaa??aaiiy ??aoee
aaaea aei ca?eueoaiiy ?? ia??iaea; inoaoi/ii, a?aenoaiue i?ae “o?oaeaie”
iaai?oiiai iioieo ia?aaeuo? oa?aeoa?iee ianooaa ( 1/M, ? eiaeia a?/ei
?icaeaa?oueny o iiiaeeiieo aeo?iao iieueiao eiio?ao?aoe?th. No?ee?noue
aeo?iai? nenoaie iie?a caaacia/o?oueny caa?aaeaiiyi iaai?oiiai iioieo.
Oaeei /eiii, i?e aenie?e oaiia?aoo?? aaeooi oiiieia?/ii-ianeaii?
eae?a?oaaeueii? oai??? ? nenoaiith ?cieueiaaieo aeo??a, noi?iiaaieo ?c
aethiiieo iie?a.

O caeeth/aii? aeeeaaeaii iniiai? aeniiaee ? ?acoeueoaoe, ui io?eiai? o
aeena?oaoe??:

O aeaiaei??i?e oai??? ssiaa–I?eena c /a?i-naeiii?anueeei /eaiii
ciaeaeaii niaeo? ??aiyiue ?ooo aeey ianeaieo aethiiieo iie?a o
iino?eiiio aaaeaaiio iaai?oiiio iie?. Anoaiiaeaii, ui i?enooi?noue iane
m eae?a?oaaeueieo iie?a caaea? ii??a aaia?aoe?? oao?iiii? iiaee H0 =
m2/4g ; a iieyo, iaioeo oeueiai cia/aiiy, niaeo? ? noaa?eueiei.

A iaeiiiaoeaaiio iaaeeaeaii? ia/eneaii iaoiaeii i?aenoiiaoaaiiy niaeo?o
aoaeoeaiee iioaioe?ae aeaiaei??ii? SU(2) aethiaeeiai?ee c
/a?i-naeiii?anueeith ianith o ciai?oiueiio aaaeaaiio iaeii??aeiiio
iaaieoiiio iie?. Aea/aii aeanoeaino? Veff i?e ??cieo cia/aiiyo m oa H.
Aeiaaaeaii, ui i?e aoaeue-yeiio m aeiaaeueiee i?i?ioi Veff
a?aeiia?aea? iaioeueiaiio iaai?oiiio iieth. sseui aaee/eia iane
ia?aaeuo? e?eoe/ia cia/aiiy mc, oyaia /anoeia aoaeoeaiiai iioaioe?aeo a
i?i?ioi? aei??aith? ioeth, ? iaiaai?/aiee aaeooi ? noaa?eueiei.

Ciaeaeaii, ui iayai?noue oiiieia?/ii? iane eae?a?oaaeueieo iie?a
ni?e/eiy? iiaee iaoai?ci aaia?aoe?? aaeooiiiai aethiiiiai eiiaeainaoo.
Oeae iaoai?ci ? a?aei?iiei a?ae eiiaeainaoe?? oao?iiieo iiae ?
?aae?co?oueny a iaai?oieo iieyo, ieae/eo ii?iaa ianoaa?eueiino? a
niaeo?? aethii?a.

Aeiaaaeaii, ui o aaeooi? noai?th?oueny ia??iaee/ia no?oeoo?a c
(eieuei?iaeo) aeaeo?e/iiai oa iaai?oiiai iie?a. Ia a?aei?io a?ae
aeaeo?ineaaei? oai??? aaia?aoe?y o?eueee iaai?oiiai eiiaeainaoo
iaiiaeeeaa. Oey eiio?ao?aoe?y ? ?ica’yceii ??aiyiue ?ooo, ui io?eiaia
iaoiaeii oai??? cao?aiue aeey iaeeo m, ? aia?aaoe/ii ia?aaaaeia
ii??aiyii c iaeii??aeiei iaai?oiei iieai. Ca aeiiiiiaith /enaeueieo
?ic?aooie?a aeiaaaeaii, ui ?aae?co?oueny o?eeooia ??aoea c ia??iaeii
(1/m. Iaai?oiee iio?e ne??cue a?/ei ? eaaioiaaiei; ca?yae ?iciiae?eaiee
ia??iaee/ii oaeei /eiii, ui aaeooi ? iaeo?aeueiei.

Iieacaii, ui aecia/aeueiei oaeoi?ii ?aae?caoe?? aaeooiii? no?oeoo?e ?
i?enooi?noue iane aethiiieo iie?a. sseui iieeanoe m = 0, oi
eiiaeainaoe?? eae?a?oaaeueieo iie?a ia a?aeaoaa?oueny. I?e H = 0
??aoeiaa eiio?ao?aoe?y ia? a?ae’?iio aia?a?th ? iiaea aaia?oaaoeny
niiioaiii.

Aeiaaaeaii aaaeeeao ?ieue eiiiiiaioe iioaioe?aea A0 aeey aecia/aiiy
aeanoeainoae ianeaieo eae?a?oaaeueieo iie?a. Ia/eneaii aoaeoeaiee
eaa?aiae?ai i?e ne?i/aii?e oaiia?aoo??, ui a?aoiao? aianie aeaaa?anueei?
iane. C’yniaaii, ui aieea ne?i/aiii? oaiia?aoo?e ia aaeooiio ??aoeo ia ?
nooo?aei o iaeano? T ( m, aea ia?oo?aaoeaiee i?aeo?ae ? aaeaeaaoiei.
C?inoaiiy oaiia?aoo?e aaaea aei ca?eueoaiiy aiie?ooaee eiiaeainaoo oa
ia??iaeo no?oeoo?e, ui a?i oi?io?.

. Oi/eiaee ca?yae i?enooi?e o oeaio?? aeoi?o, ioi/aiee ?iciiae?eaiei
ca?yaeii ?ioiai ciaeo; nenoaia iie?a o oe?eiio ? iaeo?aeueiith.
Eiio?ao?aoe?y ? no?eeith caaaeyee caa?aaeaiith iaai?oiiai iioieo.

Anoaiiaeaii, ui aeo?iaee ?ica’ycie ia? ??ciee o?ce/iee ci?no caeaaeii
a?ae ni?aa?aeiioaiiy i?ae ( ( gT2 oa m. Eiee ( < m, aia?a?y aeoi?o iiceoeaia, ? a?i iieno? nie?oiiia /anoeiei-iiae?aia caoaeaeaiiy aaeooiii? ??aoee. O cai?ioiueiio aeiaaeeo, ( > m, aia?a?y ?
a?ae’?iiith, ? oey nenoaia iie?a a?aeiia?aea? iniiaiiio noaio iiaeae?.
Aeoi? iiaeia ?icaeyaeaoe ye ?acoeueoao iaa??aaiiy ia??iaee/ii? no?oeoo?e
aaeooio; ?c c?inoaiiyi ia??iaea ??aoee aaeooiia eiio?ao?aoe?y i?e
aenie?e oaiia?aoo?? ia?aoai?th?oueny ia nenoaio ?cieueiaaieo aeo??a.

O aeiaeaoeao iaaaaeaii aeaye? iaoaiaoe/i? ia/eneaiiy, ui aoee aeiouai? a
iniiaiiio oaeno? aeena?oaoe?? c iaoith caa?aaeaiiy ?aeiino? oa noeneino?
aeeeaaeaiiy iaoa??aeo, a oaeiae aeia?aeeia? iaoa??aee oa oi?ioee, ui
aeei?enoiaothoueny a ?iaio?.

Nienie ioae?eaoe?e ca oaiith aeena?oaoe??:

Neaeicoa A.A., Aeeaineee N.A., Caneaaneee A.TH. Niiioaiiay
iaiaaie/aiiinoue aaeooia SU(2)-aethiaeeiaieee n /a?i-naeiiiianeei /eaiii
// ssaea?iay oeceea. – 1993. – O.56, ? 10. – N.218–225.

Neaeicoa A.A., Aeeaineee N.A., Caneaaneee A.TH. Yeaeo?iiaaieoiay
no?oeoo?a aaeooia aeaoia?iie oai?ee ssiaa–Ieeena n /a?i-naeiiiianeie
iannie // AEYOO. – 1994. – O.105, ? 5. – N.1098–1107.

Skalozub V.V., Vilensky S.A., Zaslavsky A.Yu. The lattice structure of
the gluon field condensate in a theory with the Chern-Simons term //
Phys. Rev. D. – 1994. – V.50, ? 8. – P.5300–5307.

Skalozub V.V., Zaslavsky A.Yu. The vacuum of the gauge theory with the
Chern-Simons term at finite temperature // A?niee AeAeO, Na?.
O?ceea.?aae?iaeaeo?ii?ea. — 1998. – Aei.3, O.1. – N.46–54.

Skalozub V.V., Zaslavsky A.Yu. The vortex solution in the
(2+1)-dimensional Yang-Mills-Chern-Simons theory at high temperature. –
1999. – 9 p. (High Energy Physics Preprint, hep-th/9905074).

Skalozub V.V., Vilensky S.A., Zaslavsky A.Yu. Periodic electromagnetic
vacuum in the two-dimensional Yang-Mills theory with the Chern-Simons
term. – Trieste, Italy: 1993. – 7 p. (Intl. Centre for Theor. Physics
Preprint IC/93/171).

Zaslavsky A.Yu. The finite temperature vortex in the topologically
massive non-Abelian gauge theory // I?aoe? Anaoe?. eiio. “Ethaeeia ?
einiin”, naeoe?y “A?aa?oaoe?y ? ooiaeaiaioaeueia o?ceea”. –
Aei?i?iiao?ianuee. – 1999. – N. 20.

Caneaanueeee I.TH. Aaeooi oiiieia?/ii-ianeaieo iie?a ssiaa–I?eena i?e
ioeueia?e oa ne?i/aii?e oaiia?aoo??. – ?oeiien.

Aeena?oaoe?y ia caeiaoooy a/aiiai nooiaiy eaiaeeaeaoa
o?ceei-iaoaiaoe/ieo iaoe ca niaoe?aeuei?noth 01.04.02 – Oai?aoe/ia
o?ceea. – Aei?i?iiao?ianueeee aea?aeaaiee oieaa?neoao,
Aei?i?iiao?ianuee, 1999.

Caoeua?oueny 7 iaoeiaeo ?ia?o, o yeeo ?icaeyaeathoueny aeanoeaino?
aaeooio eae?a?oaaeueieo iie?a o 2+1 aei??ao i?e ioeueia?e oa ne?i/aii?e
oaiia?aoo?? c o?aooaaiiyi aieeao oiiieia?/ii? iane. Ia/eneaiiy
iaeiiiaoeaaiai aoaeoeaiiai aethiiiiai iioaioe?aeo a iaai?oiiio iie?
aeiaaei iiaeeea?noue noaa?e?caoe?? iiey?eciaaiiai aaeooio. Ciaeaeaii, ui
aaeooi ianeaieo eae?a?oaaeueieo iie?a ? ia??iaee/iith aeaeo?iiaai?oiith
no?oeoo?ith, ui ooai?th?oueny caaaeyee a?aee?eoiio iaoai?cio, yeee ae??
o i?enooiino? iane *a?ia–Naeiiina. Aaeooiiee ??aoeiaee eiiaeainao iiaea
aaia?oaaoeny niiioaiii o a?aenooi?noue ciai?oiueiai iaai?oiiai iiey oa
i?e ne?i/aii?e oaiia?aoo??. Iiaoaeiaaii aoaeoeaiee eaa?aiae?ai, ui
a?aoiao? aianie oaiia?aoo?ii? aeaaa?anueei? iane. Ciaeaeaii oi/iee
aeo?iaee ?ica’ycie iae?i?eieo ??aiyiue ?ooo ?c ne?i/aiiith aia?a??th.
Aeoi? iieno? /anoeiei-iiae?aia caoaeaeaiiy iaae ??aoeiaei aaeooiii aai,
i?e aenie?e oaiia?aoo??, iniiaiee noai iiaeae?.

Eeth/ia? neiaa: aaeooi eae?a?oaaeueieo iie?a, /a?i-naeiii?anueea iana,
aeaiaei??ia oai??y, oao?iiia iiaea, ??aoeiaa no?oeoo?a, aaeooiiee
eiiaeainao, ne?i/aiia oaiia?aoo?a, aoaeoeaiee eaa?aiae?ai, aeoi?
Aa?eeiniaa, oi/iee ?ica’ycie.

Zaslavsky A.Yu. The vacuum of the topologically massive Yang-Mills
fields at zero and finite temperature. – Manuscript.

Thesis for a physics and mathematics candidate degree in speciality
01.04.02 – Theoretical physics. – Dniepropetrovsk State University,
Dniepropetrovsk, 1999.

Seven scientific papers are defended dealing with the properties of the
gauge field vacuum in 2+1 dimensions at zero and finite temperaturewith
emphasis being put on the topological mass influence. The calculation of
the effective one-loop gluon potential in a magnetic field has shown the
possibility of stabilizing the vacuum polarization. The vacuum of
massive gauge field has been found to be the periodic electromagnetic
structure caused by a newly discovered mechanism that acts in the
Chern-Simons mass presence. The vacuum lattice condensate can be
generated spontaneously without external magnetic field, and persists at
finite temperature. The effective lagrangian has been built that
includes the Debye mass contribution. An exact finite energy vortex
solution to the non-linear equation of motion has been found. The vortex
corresponds either to a particle-like excitation above the lattice
vacuum or, at high temperature, to the ground state of the model.

Key words: gauge field vacuum, Chern-Simons mass, two-dimensional
theory, tachionic mode, lattice structure, vacuum condensate, finite
temperature, effective lagrangian, Abricosov’s vortex, exact solution.

Caneaaneee A.TH. Aaeooi oiiieiae/anee-ianneaiuo iieae ssiaa–Ieeena i?e
ioeaaie e eiia/iie oaiia?aoo?a. – ?oeiienue.

Aeenna?oaoeey ia nieneaiea o/aiie noaiaie eaiaeeaeaoa
oeceei-iaoaiaoe/aneeo iaoe ii niaoeeaeueiinoe 01.04.02 – Oai?aoe/aneay
oeceea. – Aeiai?iiao?ianeee ainoaea?noaaiiue oieaa?neoao,
Aeiai?iiao?iane, 1999.

; a iieyo ieaea yoiai cia/aiey niaeo? noaaeeai. A iaeiiiaoeaaii
i?eaeeaeaiee au/eneai iaoiaeii noiie?iaaiey niaeo?a yooaeoeaiue
iioaioeeae aeaoia?iie oai?ee iieae ssiaa–Ieeena n oiiieiae/aneie iannie
ai aiaoiai aaaeaaii iaaieoiii iiea H. Eco/aiu naienoaa Veff i?e
?acee/iuo cia/aieyo m e H. Iieacaii, /oi i?e ethaii m aeiaaeueiue
ieieioi yia?aee ioaa/aao iaioeaaiio iaaieoiiio iieth. A ionoonoaea iannu
iaee/ea iieiie /anoe Veff a ieieioia i?eaiaeeo e ianoaaeeueiinoe
aaeooia. Eiaaea m i?aauoaao iaeioi?ia e?eoe/aneia cia/aiea, ImVeff
ia?auaaony a ioeue. Oaeei ia?acii, iaee/ea iannu *a?ia–Naeiiina
noaaeeece?oao iiey?ecaoeeth aaeooia eaeea?iai/iuo iieae aiaoiei
iaaieoiui iieai.

. Nouanoaaiioth ?ieue a aaia?aoeee eiiaeainaoa ea?aao A0 — iioaioeeae.
Aaeooiiay eiioeao?aoeey yaeyaony ia?oo?aa- oeaiui ?aoaieai iaeeiaeiuo
o?aaiaiee aeaeaeaiey e eiaao aieaa ieceoth yia?aeth, /ai iaeii?iaeiia
iaaieoiia iiea. *eneaiiua ?an/aou iieacuaatho, /oi ieieioi yia?aee
niioaaonoaoao o?aoaieueiie ?aoaoea n ia?eiaeii ( 1/m. Iaaieoiue iioie
/a?ac y/aeeo eaaioiaai; iieiue ca?yae aaeooia ?aaai ioeth, ii eieaeueii
eaaeaeay y/aeea eiaao iieiaeeoaeueiia yae?i, ie?oaeaiiia io?eoeaoaeueiui
ca?yaeii. A ionoonoaea aiaoiaai iaaieoiiai iiey yia?aey no?oeoo?u ieaea
ioey, e iia iiaeao aaia?e?iaaoueny niiioaiii. ?aoathuei oaeoi?ii aa
ia?aciaaiey yaeyaony oiiieiae/aneay ianna eaeea?iai/iuo iieae.

I?e eiia/iie oaiia?aoo?a a niioaaonoaee n oai, /oi /a?i-naeiiiianeay
ianna i?eaiaeeo e aaia?aoeee yeaeo?e/aneiai iiey, aue au/eneai
yooaeoeaiue eaa?aiaeeai, o/eouaathuee aeeaae oaiia?aoo?iie aeaaaaaneie
iannu (. Au/eneaiea noaoe/aneiai i?aaeaea iiey?ecaoeeiiiiai iia?aoi?a
i?eaiaeeo e ?acoeueoaoo (2 ( g2T . Enneaaeiaaiea ia iniiaa iieo/aiiiai
Leff iieacaei, /oi ?aoaoi/iay nooeoo?a aaeooiiiai eiiaeainaoa ia
i?aoa?iaaaao ea/anoaaiiuo eciaiaiee, anee oaiia?aoo?a ia i?aauoaao
ianooaa oiiieiae/aneie iannu m. Iiauoaiea oaiia?aoo?u i?eaiaeeo e
oaaee/aieth ia?eiaea no?oeoo?u e ?inoo aiieeooaeu aethiiiiai
eiiaeainaoa, i?e T >> m ia?oo?aaoeaiue iiaeoiae noaii- aeony
iaaaeaeaaoiui.

. ?aaeeaeueiia yeaeo?e/aneia e eiioeaio?e/aneia iaaieoiia iiey
ye?aie?iaaiu iannie M; ia aaneiia/iinoe eiaai /enooth eaeea?iaeo. A
oeaio?a aeo?y iaoiaeeony oi/a/iue ca?yae, ie?oaeaiiue ?ani?aaeaeaiiui
ca?yaeii i?ioeaiiieiaeiiai ciaea; a oeaeii nenoaia iieae iaeo?aeueia.
Iaaieoiue iioie /a?ac 2-ieineinoue eiia/ai; aai nio?aiaiea iaania/eaaao
onoie/eainoue eiioeao?aoeee. Nouanoaiaaiea ?aoaiey n eiia/iie yia?aeae
aiciiaeii oieueei i?e o/aoa aeeaaea aeaaaaaneie iannu. Oece/aneia
niaea?aeaiea aeo?aaie nenoaiu iieae ii?aaeaeyaony niioiioaieai iaaeaeo m
e (. I?e m > ( yoi /anoeoea-iiaeiaiia nieeoiiiia aicaoaeaeaiea
?aoaoi/iiai aaeooia n iieiaeeoaeueiie yia?aeae. I?e ( > m yia?aey aeo?y
io?eoeaoaeueia, e ii niioaaonoaoao iniiaiiio ninoiyieth, eioi?ia
yaeyaony ?acoeueoaoii iaa?aaaiey ia?eiaee/aneiai aaeooiiiai eiiaeainaoa.
I?e aunieie oaiia?aoo?a ?aoaoea i?aia?acoaony a nenoaio eciee?iaaiiuo
aeo?ae.

Eeth/aaua neiaa: aaeooi eaeea?iai/iuo iieae, /a?i-naeiiiianeay ianna,
aeaoia?iay oai?ey, oaoeiiiay iiaea, ?aoaoi/iay no?oeoo?a, aaeooiiue
eiiaeainao, eiia/iay oaiia?aoo?a, yooaeoeaiue eaa?aiaeeai, aeo?ue
Aa?eeiniaa, oi/iia ?aoaiea.

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