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inis.jinr.ruinis.jinr.ru/sl/NTBLIB/JINR-P2-85-729.pdf · 2015-04-22 · I . KBa!ITOBU8 Dp!Il!ll!!n" TeopIJI aJleMJmT8pma BSllIIWlllelcTBHII JdltKPO'l8CTHU. 1'. e . KBaH. TODIlJ! TeopIJI

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Page 1: inis.jinr.ruinis.jinr.ru/sl/NTBLIB/JINR-P2-85-729.pdf · 2015-04-22 · I . KBa!ITOBU8 Dp!Il!ll!!n" TeopIJI aJleMJmT8pma BSllIIWlllelcTBHII JdltKPO'l8CTHU. 1'. e . KBaH. TODIlJ! TeopIJI

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bullnepeaoA a lTopa

Shi rkoy DV P2 -85-729 Quan t um Pri nciples in Field In t e r actions

The concep t of quant um pri nc iple is introduced as a pri nc iple the forshymu lat ion of which is ba sed o n specific qun lu~ Ideas and notions ~e consi shyder t hrae of such princip l ~s

- the princ ip le o f quant izab i lity - t he principl e of local gauge s~etry

- the princ ip le of supersymrnrlry and their role in devel o ptlen t of the quantuo fie l d theory (QFT) Concern ilW the Fi r st o f them we ana lyze forma l aspect s and phy~lca l contents of the rcshyno~ll z4t ion procedure in QFT its relation to ultraviolet dlYergences dnd the renona-grou p The renonmallzabl li ty property formul ated as an eX i stenCe coRd i l ion of self-consistent quantum ve rsi on Wllh a ]iveh mechanl5lll of the f ield interactIon turns OIt to be equivalent to quantizab i lityl t i s ~ howo t holt the consecutlye from a hls torl c~d porflt of v i ew uie of these qtJantuln prlncip l e~ pull ~ tl l l IQrger II~ i t~t i on5 on pOs~ibla fonms of field lnt~shyract lon~

Tht illvnSlif)alion tws ~en performed a t the Labor4llory o f Theoreti cal Phy 5Ir~ JIHA

Prlrdnl or 1-1141 J oi nt Inetitute fo r trucler b rch flubna 1985

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16

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bullnepeaoA a lTopa

Shi rkoy DV P2 -85-729 Quan t um Pri nciples in Field In t e r actions

The concep t of quant um pri nc iple is introduced as a pri nc iple the forshymu lat ion of which is ba sed o n specific qun lu~ Ideas and notions ~e consi shyder t hrae of such princip l ~s

- the princ ip le o f quant izab i lity - t he principl e of local gauge s~etry

- the princ ip le of supersymrnrlry and their role in devel o ptlen t of the quantuo fie l d theory (QFT) Concern ilW the Fi r st o f them we ana lyze forma l aspect s and phy~lca l contents of the rcshyno~ll z4t ion procedure in QFT its relation to ultraviolet dlYergences dnd the renona-grou p The renonmallzabl li ty property formul ated as an eX i stenCe coRd i l ion of self-consistent quantum ve rsi on Wllh a ]iveh mechanl5lll of the f ield interactIon turns OIt to be equivalent to quantizab i lityl t i s ~ howo t holt the consecutlye from a hls torl c~d porflt of v i ew uie of these qtJantuln prlncip l e~ pull ~ tl l l IQrger II~ i t~t i on5 on pOs~ibla fonms of field lnt~shyract lon~

Tht illvnSlif)alion tws ~en performed a t the Labor4llory o f Theoreti cal Phy 5Ir~ JIHA

Prlrdnl or 1-1141 J oi nt Inetitute fo r trucler b rch flubna 1985

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(JpenpttMT OI5be[lMHVDloro ICC1MTYTa JIIAepx MCcaeao A ilYe 198)

bullnepeaoA a lTopa

Shi rkoy DV P2 -85-729 Quan t um Pri nciples in Field In t e r actions

The concep t of quant um pri nc iple is introduced as a pri nc iple the forshymu lat ion of which is ba sed o n specific qun lu~ Ideas and notions ~e consi shyder t hrae of such princip l ~s

- the princ ip le o f quant izab i lity - t he principl e of local gauge s~etry

- the princ ip le of supersymrnrlry and their role in devel o ptlen t of the quantuo fie l d theory (QFT) Concern ilW the Fi r st o f them we ana lyze forma l aspect s and phy~lca l contents of the rcshyno~ll z4t ion procedure in QFT its relation to ultraviolet dlYergences dnd the renona-grou p The renonmallzabl li ty property formul ated as an eX i stenCe coRd i l ion of self-consistent quantum ve rsi on Wllh a ]iveh mechanl5lll of the f ield interactIon turns OIt to be equivalent to quantizab i lityl t i s ~ howo t holt the consecutlye from a hls torl c~d porflt of v i ew uie of these qtJantuln prlncip l e~ pull ~ tl l l IQrger II~ i t~t i on5 on pOs~ibla fonms of field lnt~shyract lon~

Tht illvnSlif)alion tws ~en performed a t the Labor4llory o f Theoreti cal Phy 5Ir~ JIHA

Prlrdnl or 1-1141 J oi nt Inetitute fo r trucler b rch flubna 1985

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bullnepeaoA a lTopa

Shi rkoy DV P2 -85-729 Quan t um Pri nciples in Field In t e r actions

The concep t of quant um pri nc iple is introduced as a pri nc iple the forshymu lat ion of which is ba sed o n specific qun lu~ Ideas and notions ~e consi shyder t hrae of such princip l ~s

- the princ ip le o f quant izab i lity - t he principl e of local gauge s~etry

- the princ ip le of supersymrnrlry and their role in devel o ptlen t of the quantuo fie l d theory (QFT) Concern ilW the Fi r st o f them we ana lyze forma l aspect s and phy~lca l contents of the rcshyno~ll z4t ion procedure in QFT its relation to ultraviolet dlYergences dnd the renona-grou p The renonmallzabl li ty property formul ated as an eX i stenCe coRd i l ion of self-consistent quantum ve rsi on Wllh a ]iveh mechanl5lll of the f ield interactIon turns OIt to be equivalent to quantizab i lityl t i s ~ howo t holt the consecutlye from a hls torl c~d porflt of v i ew uie of these qtJantuln prlncip l e~ pull ~ tl l l IQrger II~ i t~t i on5 on pOs~ibla fonms of field lnt~shyract lon~

Tht illvnSlif)alion tws ~en performed a t the Labor4llory o f Theoreti cal Phy 5Ir~ JIHA

Prlrdnl or 1-1141 J oi nt Inetitute fo r trucler b rch flubna 1985

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21

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22

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(JpenpttMT OI5be[lMHVDloro ICC1MTYTa JIIAepx MCcaeao A ilYe 198)

bullnepeaoA a lTopa

Shi rkoy DV P2 -85-729 Quan t um Pri nciples in Field In t e r actions

The concep t of quant um pri nc iple is introduced as a pri nc iple the forshymu lat ion of which is ba sed o n specific qun lu~ Ideas and notions ~e consi shyder t hrae of such princip l ~s

- the princ ip le o f quant izab i lity - t he principl e of local gauge s~etry

- the princ ip le of supersymrnrlry and their role in devel o ptlen t of the quantuo fie l d theory (QFT) Concern ilW the Fi r st o f them we ana lyze forma l aspect s and phy~lca l contents of the rcshyno~ll z4t ion procedure in QFT its relation to ultraviolet dlYergences dnd the renona-grou p The renonmallzabl li ty property formul ated as an eX i stenCe coRd i l ion of self-consistent quantum ve rsi on Wllh a ]iveh mechanl5lll of the f ield interactIon turns OIt to be equivalent to quantizab i lityl t i s ~ howo t holt the consecutlye from a hls torl c~d porflt of v i ew uie of these qtJantuln prlncip l e~ pull ~ tl l l IQrger II~ i t~t i on5 on pOs~ibla fonms of field lnt~shyract lon~

Tht illvnSlif)alion tws ~en performed a t the Labor4llory o f Theoreti cal Phy 5Ir~ JIHA

Prlrdnl or 1-1141 J oi nt Inetitute fo r trucler b rch flubna 1985

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bullnepeaoA a lTopa

Shi rkoy DV P2 -85-729 Quan t um Pri nciples in Field In t e r actions

The concep t of quant um pri nc iple is introduced as a pri nc iple the forshymu lat ion of which is ba sed o n specific qun lu~ Ideas and notions ~e consi shyder t hrae of such princip l ~s

- the princ ip le o f quant izab i lity - t he principl e of local gauge s~etry

- the princ ip le of supersymrnrlry and their role in devel o ptlen t of the quantuo fie l d theory (QFT) Concern ilW the Fi r st o f them we ana lyze forma l aspect s and phy~lca l contents of the rcshyno~ll z4t ion procedure in QFT its relation to ultraviolet dlYergences dnd the renona-grou p The renonmallzabl li ty property formul ated as an eX i stenCe coRd i l ion of self-consistent quantum ve rsi on Wllh a ]iveh mechanl5lll of the f ield interactIon turns OIt to be equivalent to quantizab i lityl t i s ~ howo t holt the consecutlye from a hls torl c~d porflt of v i ew uie of these qtJantuln prlncip l e~ pull ~ tl l l IQrger II~ i t~t i on5 on pOs~ibla fonms of field lnt~shyract lon~

Tht illvnSlif)alion tws ~en performed a t the Labor4llory o f Theoreti cal Phy 5Ir~ JIHA

Prlrdnl or 1-1141 J oi nt Inetitute fo r trucler b rch flubna 1985

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22

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bullnepeaoA a lTopa

Shi rkoy DV P2 -85-729 Quan t um Pri nciples in Field In t e r actions

The concep t of quant um pri nc iple is introduced as a pri nc iple the forshymu lat ion of which is ba sed o n specific qun lu~ Ideas and notions ~e consi shyder t hrae of such princip l ~s

- the princ ip le o f quant izab i lity - t he principl e of local gauge s~etry

- the princ ip le of supersymrnrlry and their role in devel o ptlen t of the quantuo fie l d theory (QFT) Concern ilW the Fi r st o f them we ana lyze forma l aspect s and phy~lca l contents of the rcshyno~ll z4t ion procedure in QFT its relation to ultraviolet dlYergences dnd the renona-grou p The renonmallzabl li ty property formul ated as an eX i stenCe coRd i l ion of self-consistent quantum ve rsi on Wllh a ]iveh mechanl5lll of the f ield interactIon turns OIt to be equivalent to quantizab i lityl t i s ~ howo t holt the consecutlye from a hls torl c~d porflt of v i ew uie of these qtJantuln prlncip l e~ pull ~ tl l l IQrger II~ i t~t i on5 on pOs~ibla fonms of field lnt~shyract lon~

Tht illvnSlif)alion tws ~en performed a t the Labor4llory o f Theoreti cal Phy 5Ir~ JIHA

Prlrdnl or 1-1141 J oi nt Inetitute fo r trucler b rch flubna 1985

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bullnepeaoA a lTopa

Shi rkoy DV P2 -85-729 Quan t um Pri nciples in Field In t e r actions

The concep t of quant um pri nc iple is introduced as a pri nc iple the forshymu lat ion of which is ba sed o n specific qun lu~ Ideas and notions ~e consi shyder t hrae of such princip l ~s

- the princ ip le o f quant izab i lity - t he principl e of local gauge s~etry

- the princ ip le of supersymrnrlry and their role in devel o ptlen t of the quantuo fie l d theory (QFT) Concern ilW the Fi r st o f them we ana lyze forma l aspect s and phy~lca l contents of the rcshyno~ll z4t ion procedure in QFT its relation to ultraviolet dlYergences dnd the renona-grou p The renonmallzabl li ty property formul ated as an eX i stenCe coRd i l ion of self-consistent quantum ve rsi on Wllh a ]iveh mechanl5lll of the f ield interactIon turns OIt to be equivalent to quantizab i lityl t i s ~ howo t holt the consecutlye from a hls torl c~d porflt of v i ew uie of these qtJantuln prlncip l e~ pull ~ tl l l IQrger II~ i t~t i on5 on pOs~ibla fonms of field lnt~shyract lon~

Tht illvnSlif)alion tws ~en performed a t the Labor4llory o f Theoreti cal Phy 5Ir~ JIHA

Prlrdnl or 1-1141 J oi nt Inetitute fo r trucler b rch flubna 1985

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22

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bullnepeaoA a lTopa

Shi rkoy DV P2 -85-729 Quan t um Pri nciples in Field In t e r actions

The concep t of quant um pri nc iple is introduced as a pri nc iple the forshymu lat ion of which is ba sed o n specific qun lu~ Ideas and notions ~e consi shyder t hrae of such princip l ~s

- the princ ip le o f quant izab i lity - t he principl e of local gauge s~etry

- the princ ip le of supersymrnrlry and their role in devel o ptlen t of the quantuo fie l d theory (QFT) Concern ilW the Fi r st o f them we ana lyze forma l aspect s and phy~lca l contents of the rcshyno~ll z4t ion procedure in QFT its relation to ultraviolet dlYergences dnd the renona-grou p The renonmallzabl li ty property formul ated as an eX i stenCe coRd i l ion of self-consistent quantum ve rsi on Wllh a ]iveh mechanl5lll of the f ield interactIon turns OIt to be equivalent to quantizab i lityl t i s ~ howo t holt the consecutlye from a hls torl c~d porflt of v i ew uie of these qtJantuln prlncip l e~ pull ~ tl l l IQrger II~ i t~t i on5 on pOs~ibla fonms of field lnt~shyract lon~

Tht illvnSlif)alion tws ~en performed a t the Labor4llory o f Theoreti cal Phy 5Ir~ JIHA

Prlrdnl or 1-1141 J oi nt Inetitute fo r trucler b rch flubna 1985

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SO lIane AOOTII OJtlIOIlH8lHOlO ollJlC8llllS po B31l111OJAelCTBlll 1tB8lIshy

bull 0BlIX 000 B o611B011l )lOCT8tOIII0 BWoo Keprlll

Tew C8IIIDI B09111Oamp8O ns HllIIIIX rJJ83U H8qm8H OcyJleCTlllUftshy

C8 M81fT9 alHll1elJta naee laquolew n0JIYB8KOBOI JUlBHOCft bull bullbull bull MY

XOTD He TOJIlgtIltO HOn 18K y01poell8 OpllPOAB ( II npcllCXOJlllt

trpIlpoJDtHB JmeHU) r 80 bull 00 803MIlampHOOH llOOTW1b ~ llaquo)Se1 6Y1ltl

YlODBlecbullbull ApaROI 18 II1I)I - YBHBU noqetq Il)aPOAB lIIWI8CJI

ftMOHRO lalltOl a He lJJYtol2I bull

20

KaJt YSI OTMIlQaOClgt IICO qeH njllUDlKIlll - 1IlI IIKC eye cmr - no coool DptfponG RBImrOa HltaHMmuat TaR KBY JllR HX

ltIxgt ptqUPOBKl HOo6xo_ lltoro KIJ8HIOBIlt nOHllTlIR

DOIDmIe ltfJa3H 8OJOIoooI ltfJYHKUIII R He33BHellMOeTH OT Hee H86shy

AI11taOMWC BeAMRIi

nOHJIIRO 0 paSJIiltOlllX KB8ltlOBUX ClOTilcmuwx B 0 (1030- H

~JlIIll-l1l4IlX

OOlurroe deg nponcxotlllellltll bull CTPYKTYpc YJJJgtpaqmMOlOBWlt pocshy

XOJDlllaquo)CTeA B IQlaJITOIlOA TCOpllll UOIUI bull 0 II]lIlllllAYpe nepellopltl1polgtshy

til bull

Kwt Mll y6~ltWDCL nOCJI9JlOMlCJI1dIOe lUl[J0JI30BQUlle 3TUI

KBaliTOBW DpIIJillHUOB BBObullbullbull MOOIIYll Jtere_CTHcelYll O1pyn B

up KBWl1OBUX SlMeHB KOlOpwt II OCHOBe cnoel nO)tlHUen CTBTJlCTHshy

qeOKlDt 38SOHOlampePUOCTfDII

JlnepaTYpa

1 IilJlPKOlI I(l SW 1983 H 1063-1072

2 JljpaJ [[AM UpJllUDlJlW ItBlUrroBOI MBXIUlHIOI Iayxa II bullbull I~9

c 4(13 1Jy1I tdl3JIItJI JueprooT0I0III9JIIT M 19I13 0 4G

J tSooft G Phyenalao R~port s 1Q84 1]1 1~_I)~

4 Nnmbu y Ph61 cft Ne~ort8 1994 l2 2)7- 8

5 Gultat50n T Arkl v ( Watb 4strJys 1)46 )A 2 t

Spbullbull B R JllalhlIl7obullbull1968 l bull 1404

6 tJtloort Q VeltallUl)l Nuol Fhyens t 1972 i1 J131

7 CoOoJlo C n ila7c c60plllUt 1936 T ~ c 39

6 Sailwllrll L Tb1 rr Itl8 ltt1Itrlbutlo41IAlnDd Poria 1950

9 SoIWlllOOD lUI nape OC 1957 Ao a _h lZ 227

21

10 Bor0JID60B HB R IIJIpKOB nB BBeJ(eHHe Jl TeoPIJll KBIIJlTOBaHBHX

nonea U3Q3-sBayxa M IIrn6 ~ 113ll4-et Hayxa N 1$4

sectsect 2930 11 Coleman So Weinberg I Phybullbull Royo D 1973 ~ 1888-191 0

12 fiIlp Il Il H Jij) lB 1982 T 35 c 1221

13 Bop U Pbybullbull Rbullbullbull 1935 ~ p 696-702 DopeBOll COl ihlJoo Bop 1l00)lOJlHlie Tp)tll T2 HayRa M bull bull 197I oIB(-I91 Bop U lIa6paH1Dle Tp)tll ~ 2 11ayKa 101 19710526-532

14 Shirkov D V In onlineAl and Turbul ent ProaOS888 in Pb1 shySampgd R Z HampMrood AcadPubl II Y81 cmiddot vol bull bull eI bull

1964 p 16)71 IlAII CCCP 1982 263 c 64-67

15 Bor0JID6oB HR bull mwpKOJl nB bull IlAH OCCP 1955 ~ 103 o al3-al6

16 Biuok~bra EC Peterann A HelyPhTbullbull Aot 1953 y~ p 49~520

17 Gell-aampDn a Lo_ 7 PbJbullbull lev 1954 v~ p 1)00-1)

lS W1180n X aev MOdb7ao 19BJ 22 p 58)-599

19 r OJlloltlgtUUt IlA Ilnu Bn n0l0IIIIl B J)iqI 19I 13 452

20 Parkbullbull A and wbullbull t P bya Let t 1984 v ~ p 99-104

21 31bmTeIJ 1 0 cOIIIUeHHOM OOCTOIIBIIl ~eoP nam - COOp HBrUI TPJIlOB T~ HayJca Yo 1966 c245

PyxOUlC OOCl)1IIWI B H bull lM9JIlocKHll OTlleJI

9 OKI86p~ 1985 rollB

22

bull

W~DK08 aB P2-85-729 KBaHTOB~e np~H~~n~ 80 B3a~MOaeHCT8~~X none~

B80A~TC~ nOH~THe KsaHT080iO np~HUHna KaK npHH~Hna npH OOpM ynHpO BKe KOshy

Topo r o c~ecT8eHHO Hc nOnb3y~Tc~ KBaHTOB~e npeACTaaneHHA H cneUH~H~eCKHe KBaHTOB~e nO~THR Pacc~aTPH8aeTCA ponb Tpex TaKHX n pHHUHnOB

npHHUHna nepeHopHHpyeHocT H HH a4e - KsaHTyeMOC t H - npHHUHna noKanbHoM KanH6poe04HOH cHHHeTpHH - nplo HlI lo1 nA cynepcH_eTp IoH1

B pa3SK TH H K8aHTOBOH TeopHH no~ B CBA3K C nepeWM 1013 3THX npHHUHnoe aHan]H py~ l CR eop-nbHaR CTopoMa CH 3H4eCKOC COAep~HHe npo ue AYPW ncpcHopHHpo eOK 8 KTn ee C8A3 b ~ HanH~HpoundM ynbTpacentHonCTOBWX p aC XOAHHOCTeM H pe HOPMr pynnoH n p HH UH n nepeHOOHHpyeMOcTH OOPMynHPyeMWM KaK rpe60aHHe c~eCTBoeaHHA BHyT shypeHH e HenpoTH Bope wHaOM Ka~TOBO~ epc~~ A~HHO~ ~~eJ~ B3aHHoAe~cTHM non~

oKa3BaeTC~ 3KBHBaneM THhUoI YCI108HO KII3 HTyCHOC TW nH K IIHrOBOC T~I nCUC83aHO ~TO noc~AOaTenbMoe B HCTo~~eCKOH nnaMe kcnonb 308aH~e Tpex KBaHToswx np~I ILllolnOA Dce 60nee orpilM~4H9aeT B03 MOlliHbH AHlfUMo14 eC tue Mex3HH3MbI 83aHMO shyAe~cT8H~ KBaHTOB~X noneK

P~60Ta awnonHeHa B fla60paToDHH Teope TH4e~KOM ~H3HKH OHRH

(JpenpttMT OI5be[lMHVDloro ICC1MTYTa JIIAepx MCcaeao A ilYe 198)

bullnepeaoA a lTopa

Shi rkoy DV P2 -85-729 Quan t um Pri nciples in Field In t e r actions

The concep t of quant um pri nc iple is introduced as a pri nc iple the forshymu lat ion of which is ba sed o n specific qun lu~ Ideas and notions ~e consi shyder t hrae of such princip l ~s

- the princ ip le o f quant izab i lity - t he principl e of local gauge s~etry

- the princ ip le of supersymrnrlry and their role in devel o ptlen t of the quantuo fie l d theory (QFT) Concern ilW the Fi r st o f them we ana lyze forma l aspect s and phy~lca l contents of the rcshyno~ll z4t ion procedure in QFT its relation to ultraviolet dlYergences dnd the renona-grou p The renonmallzabl li ty property formul ated as an eX i stenCe coRd i l ion of self-consistent quantum ve rsi on Wllh a ]iveh mechanl5lll of the f ield interactIon turns OIt to be equivalent to quantizab i lityl t i s ~ howo t holt the consecutlye from a hls torl c~d porflt of v i ew uie of these qtJantuln prlncip l e~ pull ~ tl l l IQrger II~ i t~t i on5 on pOs~ibla fonms of field lnt~shyract lon~

Tht illvnSlif)alion tws ~en performed a t the Labor4llory o f Theoreti cal Phy 5Ir~ JIHA

Prlrdnl or 1-1141 J oi nt Inetitute fo r trucler b rch flubna 1985

Page 11: inis.jinr.ruinis.jinr.ru/sl/NTBLIB/JINR-P2-85-729.pdf · 2015-04-22 · I . KBa!ITOBU8 Dp!Il!ll!!n" TeopIJI aJleMJmT8pma BSllIIWlllelcTBHII JdltKPO'l8CTHU. 1'. e . KBaH. TODIlJ! TeopIJI

1 IIepexoA OJ lltBIIHoBOI IIOXaKJtICJl R DepeRO~pyelOJR _shy

TOBOR TeOpm DOJIJI ( yln npllJUWUl 1Dl) njllIBQJl K tOtq 110 BBllSH

lIYHlWBORM1gtlI01O npo9BO110 X8pa~DJlIYlO noeJl1DtWIIJlol ijJyrutshy

JSol t WY nanylpoundllm JIJIm 1l000P OpB3BOJ1bHHX DOClOJUIllla - ltOHCfSHr

CM3R

2 yqe D]lIIlUUI8 IKC 0 meJIellBo Ilt8lIlWPOIlOIIUO OMO

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~ ROHCTaDT 838JOOJAelcTBItII ASHHOlO 1WllI6pollOIIUl1O nltlJlJi

deg n pD

J Ieno_o nplIHlUIIIB eyea BBOJIa 8IIome OnplUl8JI8ll1Di

1l860pu ooeTOlIIIIe gaR lI3 60 aK 3 4eplOl-DOJlel (eynepshy

tqJUTlWlelll) SIIIDIDAea01BllJI lltOOplll[ ODBeWlSllCJI ollllllODellKol

IltOHOURO eM bullbull bull

liaKoaOD OpeACT8IWIOlCJI BeeWOi eMlJAlWOl neponelmlllS

eI1O aTona

4 liaJIOlIlHle pe60B8IIIB eBDplIllepoHoplOlP1elOJ01II ( nPKHIUIll

CIDl DOHIIIIIIOa 10 YeJlOBBO oayTeTllllll YJIgtTJl84DI~OT08HX paoshy

lroJ1)llllce B 1I01I8lIJD( oollo)ll8UX paClrOAJDS)01II no 4oJlMlJlHIN

n~3HaKaM C~eTQ cTonoHol D~e H ax npoKaBO~ D ~Qrp8HKRQ-

He) DJlI 3aA111HO 9118qemm emma Yl8CtBYUIIIIX lSOTBl1 4aultCllpye

CYDepc_pIIIllYD 1OO1leu nMIlI8I OTO erwl p8BItII)I JtIIY)I DMYshy

SO lIane AOOTII OJtlIOIlH8lHOlO ollJlC8llllS po B31l111OJAelCTBlll 1tB8lIshy

bull 0BlIX 000 B o611B011l )lOCT8tOIII0 BWoo Keprlll

Tew C8IIIDI B09111Oamp8O ns HllIIIIX rJJ83U H8qm8H OcyJleCTlllUftshy

C8 M81fT9 alHll1elJta naee laquolew n0JIYB8KOBOI JUlBHOCft bull bullbull bull MY

XOTD He TOJIlgtIltO HOn 18K y01poell8 OpllPOAB ( II npcllCXOJlllt

trpIlpoJDtHB JmeHU) r 80 bull 00 803MIlampHOOH llOOTW1b ~ llaquo)Se1 6Y1ltl

YlODBlecbullbull ApaROI 18 II1I)I - YBHBU noqetq Il)aPOAB lIIWI8CJI

ftMOHRO lalltOl a He lJJYtol2I bull

20

KaJt YSI OTMIlQaOClgt IICO qeH njllUDlKIlll - 1IlI IIKC eye cmr - no coool DptfponG RBImrOa HltaHMmuat TaR KBY JllR HX

ltIxgt ptqUPOBKl HOo6xo_ lltoro KIJ8HIOBIlt nOHllTlIR

DOIDmIe ltfJa3H 8OJOIoooI ltfJYHKUIII R He33BHellMOeTH OT Hee H86shy

AI11taOMWC BeAMRIi

nOHJIIRO 0 paSJIiltOlllX KB8ltlOBUX ClOTilcmuwx B 0 (1030- H

~JlIIll-l1l4IlX

OOlurroe deg nponcxotlllellltll bull CTPYKTYpc YJJJgtpaqmMOlOBWlt pocshy

XOJDlllaquo)CTeA B IQlaJITOIlOA TCOpllll UOIUI bull 0 II]lIlllllAYpe nepellopltl1polgtshy

til bull

Kwt Mll y6~ltWDCL nOCJI9JlOMlCJI1dIOe lUl[J0JI30BQUlle 3TUI

KBaliTOBW DpIIJillHUOB BBObullbullbull MOOIIYll Jtere_CTHcelYll O1pyn B

up KBWl1OBUX SlMeHB KOlOpwt II OCHOBe cnoel nO)tlHUen CTBTJlCTHshy

qeOKlDt 38SOHOlampePUOCTfDII

JlnepaTYpa

1 IilJlPKOlI I(l SW 1983 H 1063-1072

2 JljpaJ [[AM UpJllUDlJlW ItBlUrroBOI MBXIUlHIOI Iayxa II bullbull I~9

c 4(13 1Jy1I tdl3JIItJI JueprooT0I0III9JIIT M 19I13 0 4G

J tSooft G Phyenalao R~port s 1Q84 1]1 1~_I)~

4 Nnmbu y Ph61 cft Ne~ort8 1994 l2 2)7- 8

5 Gultat50n T Arkl v ( Watb 4strJys 1)46 )A 2 t

Spbullbull B R JllalhlIl7obullbull1968 l bull 1404

6 tJtloort Q VeltallUl)l Nuol Fhyens t 1972 i1 J131

7 CoOoJlo C n ila7c c60plllUt 1936 T ~ c 39

6 Sailwllrll L Tb1 rr Itl8 ltt1Itrlbutlo41IAlnDd Poria 1950

9 SoIWlllOOD lUI nape OC 1957 Ao a _h lZ 227

21

10 Bor0JID60B HB R IIJIpKOB nB BBeJ(eHHe Jl TeoPIJll KBIIJlTOBaHBHX

nonea U3Q3-sBayxa M IIrn6 ~ 113ll4-et Hayxa N 1$4

sectsect 2930 11 Coleman So Weinberg I Phybullbull Royo D 1973 ~ 1888-191 0

12 fiIlp Il Il H Jij) lB 1982 T 35 c 1221

13 Bop U Pbybullbull Rbullbullbull 1935 ~ p 696-702 DopeBOll COl ihlJoo Bop 1l00)lOJlHlie Tp)tll T2 HayRa M bull bull 197I oIB(-I91 Bop U lIa6paH1Dle Tp)tll ~ 2 11ayKa 101 19710526-532

14 Shirkov D V In onlineAl and Turbul ent ProaOS888 in Pb1 shySampgd R Z HampMrood AcadPubl II Y81 cmiddot vol bull bull eI bull

1964 p 16)71 IlAII CCCP 1982 263 c 64-67

15 Bor0JID6oB HR bull mwpKOJl nB bull IlAH OCCP 1955 ~ 103 o al3-al6

16 Biuok~bra EC Peterann A HelyPhTbullbull Aot 1953 y~ p 49~520

17 Gell-aampDn a Lo_ 7 PbJbullbull lev 1954 v~ p 1)00-1)

lS W1180n X aev MOdb7ao 19BJ 22 p 58)-599

19 r OJlloltlgtUUt IlA Ilnu Bn n0l0IIIIl B J)iqI 19I 13 452

20 Parkbullbull A and wbullbull t P bya Let t 1984 v ~ p 99-104

21 31bmTeIJ 1 0 cOIIIUeHHOM OOCTOIIBIIl ~eoP nam - COOp HBrUI TPJIlOB T~ HayJca Yo 1966 c245

PyxOUlC OOCl)1IIWI B H bull lM9JIlocKHll OTlleJI

9 OKI86p~ 1985 rollB

22

bull

W~DK08 aB P2-85-729 KBaHTOB~e np~H~~n~ 80 B3a~MOaeHCT8~~X none~

B80A~TC~ nOH~THe KsaHT080iO np~HUHna KaK npHH~Hna npH OOpM ynHpO BKe KOshy

Topo r o c~ecT8eHHO Hc nOnb3y~Tc~ KBaHTOB~e npeACTaaneHHA H cneUH~H~eCKHe KBaHTOB~e nO~THR Pacc~aTPH8aeTCA ponb Tpex TaKHX n pHHUHnOB

npHHUHna nepeHopHHpyeHocT H HH a4e - KsaHTyeMOC t H - npHHUHna noKanbHoM KanH6poe04HOH cHHHeTpHH - nplo HlI lo1 nA cynepcH_eTp IoH1

B pa3SK TH H K8aHTOBOH TeopHH no~ B CBA3K C nepeWM 1013 3THX npHHUHnoe aHan]H py~ l CR eop-nbHaR CTopoMa CH 3H4eCKOC COAep~HHe npo ue AYPW ncpcHopHHpo eOK 8 KTn ee C8A3 b ~ HanH~HpoundM ynbTpacentHonCTOBWX p aC XOAHHOCTeM H pe HOPMr pynnoH n p HH UH n nepeHOOHHpyeMOcTH OOPMynHPyeMWM KaK rpe60aHHe c~eCTBoeaHHA BHyT shypeHH e HenpoTH Bope wHaOM Ka~TOBO~ epc~~ A~HHO~ ~~eJ~ B3aHHoAe~cTHM non~

oKa3BaeTC~ 3KBHBaneM THhUoI YCI108HO KII3 HTyCHOC TW nH K IIHrOBOC T~I nCUC83aHO ~TO noc~AOaTenbMoe B HCTo~~eCKOH nnaMe kcnonb 308aH~e Tpex KBaHToswx np~I ILllolnOA Dce 60nee orpilM~4H9aeT B03 MOlliHbH AHlfUMo14 eC tue Mex3HH3MbI 83aHMO shyAe~cT8H~ KBaHTOB~X noneK

P~60Ta awnonHeHa B fla60paToDHH Teope TH4e~KOM ~H3HKH OHRH

(JpenpttMT OI5be[lMHVDloro ICC1MTYTa JIIAepx MCcaeao A ilYe 198)

bullnepeaoA a lTopa

Shi rkoy DV P2 -85-729 Quan t um Pri nciples in Field In t e r actions

The concep t of quant um pri nc iple is introduced as a pri nc iple the forshymu lat ion of which is ba sed o n specific qun lu~ Ideas and notions ~e consi shyder t hrae of such princip l ~s

- the princ ip le o f quant izab i lity - t he principl e of local gauge s~etry

- the princ ip le of supersymrnrlry and their role in devel o ptlen t of the quantuo fie l d theory (QFT) Concern ilW the Fi r st o f them we ana lyze forma l aspect s and phy~lca l contents of the rcshyno~ll z4t ion procedure in QFT its relation to ultraviolet dlYergences dnd the renona-grou p The renonmallzabl li ty property formul ated as an eX i stenCe coRd i l ion of self-consistent quantum ve rsi on Wllh a ]iveh mechanl5lll of the f ield interactIon turns OIt to be equivalent to quantizab i lityl t i s ~ howo t holt the consecutlye from a hls torl c~d porflt of v i ew uie of these qtJantuln prlncip l e~ pull ~ tl l l IQrger II~ i t~t i on5 on pOs~ibla fonms of field lnt~shyract lon~

Tht illvnSlif)alion tws ~en performed a t the Labor4llory o f Theoreti cal Phy 5Ir~ JIHA

Prlrdnl or 1-1141 J oi nt Inetitute fo r trucler b rch flubna 1985

Page 12: inis.jinr.ruinis.jinr.ru/sl/NTBLIB/JINR-P2-85-729.pdf · 2015-04-22 · I . KBa!ITOBU8 Dp!Il!ll!!n" TeopIJI aJleMJmT8pma BSllIIWlllelcTBHII JdltKPO'l8CTHU. 1'. e . KBaH. TODIlJ! TeopIJI

10 Bor0JID60B HB R IIJIpKOB nB BBeJ(eHHe Jl TeoPIJll KBIIJlTOBaHBHX

nonea U3Q3-sBayxa M IIrn6 ~ 113ll4-et Hayxa N 1$4

sectsect 2930 11 Coleman So Weinberg I Phybullbull Royo D 1973 ~ 1888-191 0

12 fiIlp Il Il H Jij) lB 1982 T 35 c 1221

13 Bop U Pbybullbull Rbullbullbull 1935 ~ p 696-702 DopeBOll COl ihlJoo Bop 1l00)lOJlHlie Tp)tll T2 HayRa M bull bull 197I oIB(-I91 Bop U lIa6paH1Dle Tp)tll ~ 2 11ayKa 101 19710526-532

14 Shirkov D V In onlineAl and Turbul ent ProaOS888 in Pb1 shySampgd R Z HampMrood AcadPubl II Y81 cmiddot vol bull bull eI bull

1964 p 16)71 IlAII CCCP 1982 263 c 64-67

15 Bor0JID6oB HR bull mwpKOJl nB bull IlAH OCCP 1955 ~ 103 o al3-al6

16 Biuok~bra EC Peterann A HelyPhTbullbull Aot 1953 y~ p 49~520

17 Gell-aampDn a Lo_ 7 PbJbullbull lev 1954 v~ p 1)00-1)

lS W1180n X aev MOdb7ao 19BJ 22 p 58)-599

19 r OJlloltlgtUUt IlA Ilnu Bn n0l0IIIIl B J)iqI 19I 13 452

20 Parkbullbull A and wbullbull t P bya Let t 1984 v ~ p 99-104

21 31bmTeIJ 1 0 cOIIIUeHHOM OOCTOIIBIIl ~eoP nam - COOp HBrUI TPJIlOB T~ HayJca Yo 1966 c245

PyxOUlC OOCl)1IIWI B H bull lM9JIlocKHll OTlleJI

9 OKI86p~ 1985 rollB

22

bull

W~DK08 aB P2-85-729 KBaHTOB~e np~H~~n~ 80 B3a~MOaeHCT8~~X none~

B80A~TC~ nOH~THe KsaHT080iO np~HUHna KaK npHH~Hna npH OOpM ynHpO BKe KOshy

Topo r o c~ecT8eHHO Hc nOnb3y~Tc~ KBaHTOB~e npeACTaaneHHA H cneUH~H~eCKHe KBaHTOB~e nO~THR Pacc~aTPH8aeTCA ponb Tpex TaKHX n pHHUHnOB

npHHUHna nepeHopHHpyeHocT H HH a4e - KsaHTyeMOC t H - npHHUHna noKanbHoM KanH6poe04HOH cHHHeTpHH - nplo HlI lo1 nA cynepcH_eTp IoH1

B pa3SK TH H K8aHTOBOH TeopHH no~ B CBA3K C nepeWM 1013 3THX npHHUHnoe aHan]H py~ l CR eop-nbHaR CTopoMa CH 3H4eCKOC COAep~HHe npo ue AYPW ncpcHopHHpo eOK 8 KTn ee C8A3 b ~ HanH~HpoundM ynbTpacentHonCTOBWX p aC XOAHHOCTeM H pe HOPMr pynnoH n p HH UH n nepeHOOHHpyeMOcTH OOPMynHPyeMWM KaK rpe60aHHe c~eCTBoeaHHA BHyT shypeHH e HenpoTH Bope wHaOM Ka~TOBO~ epc~~ A~HHO~ ~~eJ~ B3aHHoAe~cTHM non~

oKa3BaeTC~ 3KBHBaneM THhUoI YCI108HO KII3 HTyCHOC TW nH K IIHrOBOC T~I nCUC83aHO ~TO noc~AOaTenbMoe B HCTo~~eCKOH nnaMe kcnonb 308aH~e Tpex KBaHToswx np~I ILllolnOA Dce 60nee orpilM~4H9aeT B03 MOlliHbH AHlfUMo14 eC tue Mex3HH3MbI 83aHMO shyAe~cT8H~ KBaHTOB~X noneK

P~60Ta awnonHeHa B fla60paToDHH Teope TH4e~KOM ~H3HKH OHRH

(JpenpttMT OI5be[lMHVDloro ICC1MTYTa JIIAepx MCcaeao A ilYe 198)

bullnepeaoA a lTopa

Shi rkoy DV P2 -85-729 Quan t um Pri nciples in Field In t e r actions

The concep t of quant um pri nc iple is introduced as a pri nc iple the forshymu lat ion of which is ba sed o n specific qun lu~ Ideas and notions ~e consi shyder t hrae of such princip l ~s

- the princ ip le o f quant izab i lity - t he principl e of local gauge s~etry

- the princ ip le of supersymrnrlry and their role in devel o ptlen t of the quantuo fie l d theory (QFT) Concern ilW the Fi r st o f them we ana lyze forma l aspect s and phy~lca l contents of the rcshyno~ll z4t ion procedure in QFT its relation to ultraviolet dlYergences dnd the renona-grou p The renonmallzabl li ty property formul ated as an eX i stenCe coRd i l ion of self-consistent quantum ve rsi on Wllh a ]iveh mechanl5lll of the f ield interactIon turns OIt to be equivalent to quantizab i lityl t i s ~ howo t holt the consecutlye from a hls torl c~d porflt of v i ew uie of these qtJantuln prlncip l e~ pull ~ tl l l IQrger II~ i t~t i on5 on pOs~ibla fonms of field lnt~shyract lon~

Tht illvnSlif)alion tws ~en performed a t the Labor4llory o f Theoreti cal Phy 5Ir~ JIHA

Prlrdnl or 1-1141 J oi nt Inetitute fo r trucler b rch flubna 1985