U Vikipediyi ye statti pro inshi znachennya cogo termina Propagator znachennya Propaga tor abo fu nkciya poshi rennya funkciya sho zadaye amplitudu jmovirnosti perehodu kvantovoyi chastinki yaka perebuvala v pevnij moment chasu v odniyeyi tochci prostoru v inshu v inshij moment chasu Propagator ye funkciyeyu Grina rivnyannya Shredingera Propagatori vikoristovuyutsya dlya funkcionalnogo formulyuvannya kvantovoyi mehaniki v yakomu zastosovuyutsya integrali Fejnmana Zmist 1 Oznachennya 2 Prikladi 2 1 Vilna chastinka 2 2 Propagatori u kvantovij teoriyi polya 3 Posilannya 4 LiteraturaOznachennya RedaguvatiPropagator viznachayetsya yak matrichnij element operatora evolyuciyi K x t x t x S t t x displaystyle K x t x prime t prime langle x hat S t t prime x prime rangle nbsp de propagator poznachenij K operator evolyuciyi S displaystyle hat S nbsp a x displaystyle x rangle nbsp vlasna funkciya operatora koordinati V nerelyativistskij kvantovij mehanici propagator zadovolnyaye rivnyannyu H i ℏ t K x t x t i ℏ d x x d t t displaystyle left hat H i hbar frac partial partial t right K x t x t i hbar delta x x delta t t nbsp de H displaystyle hat H nbsp gamiltonian ℏ displaystyle hbar nbsp zvedena stala Planka Hvilova funkciya chastinki v moment chasu t virazhayetsya cherez hvilovu funkciyu v moment chasu t lt t displaystyle t prime lt t nbsp z vikoristannyam propagatora cherez formulu ps x t K x t x t ps x t d x displaystyle psi x t int limits infty infty K x t x prime t prime psi x prime t prime dx prime nbsp Prikladi RedaguvatiVilna chastinka Redaguvati Dlya vilnoyi chastinki yaka ruhayetsya v trivimirnomu prostori propagator maye viglyad K r t r t K r r t t m 2 p i ℏ t t 3 2 exp i m r r 2 2 ℏ t t displaystyle K mathbf r t mathbf r prime t prime K mathbf r mathbf r prime t t prime left frac m 2 pi i hbar t t prime right 3 2 exp left frac im mathbf r mathbf r prime 2 2 hbar t t prime right nbsp de m masa chastinki Cya formula opisuye rozplivannya hvilovogo paketa z chasom Propagatori u kvantovij teoriyi polya Redaguvati Cej rozdil potrebuye dodatkovih posilan na dzherela dlya polipshennya jogo perevirnosti Bud laska dopomozhit udoskonaliti cej rozdil dodavshi posilannya na nadijni avtoritetni dzherela Zvernitsya na storinku obgovorennya za poyasnennyami ta dopomozhit vipraviti nedoliki Material bez dzherel mozhe buti piddano sumnivu ta vilucheno lipen 2015 U kvantovij teoriyi polya propagatorom dlya kovariantnogo polya narodzhennya i znishennya PS l x s d 3 p 2 p 3 2 E p a s p e i p x u l s p b s p e i p x v l s p displaystyle hat Psi l x sum sigma int frac d 3 mathbf p sqrt 2 pi 3 2E mathbf p left hat a sigma mathbf p e ipx u l sigma mathbf p hat b sigma dagger mathbf p e ipx v l sigma mathbf p right nbsp de l displaystyle l nbsp spinornij indeks sho vidpovidaye spinu spiralnosti s displaystyle s nbsp polya yak predstavlennya grupi Puankare s displaystyle sigma nbsp polyarizaciyi 2 s 1 displaystyle 2s 1 nbsp polyarizacij dlya masivnogo vipadku 1 polyarizaciya dlya bezmasovogo vipadku bez invariantnosti predstavlennya vidnosno diskretnih simetrij grupi Lorenca ta 2 polyarizaciyi dlya bezmasovogo vipadku iz invariantnistyu vidnosno vkazanih diskretnih simetrij u koordinatnomu predstavlenni nazivayetsya 1 viraz i D l m c x y 0 T PS l x PS m y 0 1 displaystyle iD lm c x y langle 0 hat T left hat Psi l x hat Psi m dagger y right 0 rangle qquad 1 nbsp Tut T A x B y 8 x 0 y 0 A x B y 8 y 0 x 0 B y A x displaystyle hat T hat A x hat B y theta x 0 y 0 hat A x hat B y pm theta y 0 x 0 hat B y hat A x nbsp de displaystyle pm nbsp obirayetsya v zalezhnosti vid tipu komutacijnih spivvidnoshen dlya operatoriv poliv A x B y displaystyle hat A x hat B y nbsp vidpovidno komutacijnih chi antikomutacijnih Obmezhimos propagatorom dlya vilnoyi teoriyi Vrahovuyuchi sho pri diyi na vakuum mayemo a 0 b 0 0 displaystyle hat a 0 rangle hat b 0 rangle 0 nbsp viraz 1 displaystyle 1 nbsp mozhna perepisati yak i D l m c x y 8 x 0 y 0 PS l x PS m y 8 y 0 x 0 PS m y PS l x 2 displaystyle iD lm c x y theta x 0 y 0 langle hat Psi l x hat Psi m dagger y pm rangle pm theta y 0 x 0 langle hat Psi m dagger y hat Psi l x pm rangle qquad 2 nbsp de displaystyle pm nbsp viznachaye antikomutator chi komutator vidpovidno Vikoristovuyuchi anti komutacijni spivvidnoshennya na operatori narodzhennya i znishennya a s p a s k b s p b s k d p k d s s a s p b s k a s p a s k 0 displaystyle hat a sigma mathbf p hat a sigma dagger mathbf k pm hat b sigma mathbf p hat b sigma dagger mathbf k pm delta mathbf p mathbf k delta sigma sigma quad hat a sigma mathbf p hat b sigma mathbf k pm hat a sigma mathbf p hat a sigma mathbf k pm 0 nbsp mozhna otrimati viraz i D l m c x y i P l m i x D c x y 3 displaystyle iD lm c x y iP lm left i frac partial partial x right D c x y qquad 3 nbsp de P l m p s u l s p u l s p displaystyle P lm left p right sum sigma u l sigma p u l sigma dagger p nbsp a D c x y i 8 x 0 y 0 D m x y i 8 y 0 x 0 D m y x D m x y d 3 p 2 p 3 2 p 0 e i p x y displaystyle D c x y i theta x 0 y 0 D m x y i theta y 0 x 0 D m y x quad D m x y int frac d 3 mathbf p 2 pi 3 2p 0 e ip x y nbsp propagator dlya klejn gordonivskogo polya spinu 0 Yak mozhna pokazati vin zadovolnyaye rivnyannyu 2 m 2 D c x y d x y displaystyle left partial 2 m 2 right D c x y delta x y nbsp tomu jogo mozhna predstaviti yak D c x y i 2 p 4 e i p x y d 4 p p 2 m 2 i 0 displaystyle D c x y frac i 2 pi 4 int frac e ip x y d 4 p p 2 m 2 i0 nbsp Tomu nareshti viraz 3 displaystyle 3 nbsp perepisuyetsya yak D l m c x y P l m i x i 2 p 4 e i p x y d 4 p p 2 m 2 i 0 i 2 p 4 P l m p e i p x y d 4 p p 2 m 2 i 0 displaystyle D lm c x y P lm left i frac partial partial x right frac i 2 pi 4 int frac e ip x y d 4 p p 2 m 2 i0 frac i 2 pi 4 int frac P lm left p right e ip x y d 4 p p 2 m 2 i0 nbsp Dlya najprostishih teorij skalyarnoyi dirakivskoyi masivnogo bozonu spinu 1 i bezmasovogo bozonu spiralnosti 1 mayemo z vidomih viraziv dlya sum po polyarizaciyam D l m s c x y D c x y i 2 p 4 e i p x y d 4 p m 2 p 2 i 0 displaystyle D lm sc x y D c x y frac i 2 pi 4 int frac e ip x y d 4 p m 2 p 2 i0 nbsp D l m d x y i 2 p 4 i g m m m e i p x y d 4 p m 2 p 2 i 0 displaystyle D lm d x y frac i 2 pi 4 i gamma mu partial mu m int frac e ip x y d 4 p m 2 p 2 i0 nbsp D l m p r x y i 2 p 4 g m n m n m 2 e i p x y d 4 p m 2 p 2 i 0 displaystyle D lm pr x y frac i 2 pi 4 left g mu nu frac partial mu partial nu m 2 right int frac e ip x y d 4 p m 2 p 2 i0 nbsp D l m e l x y i 2 p 4 g m n e i p x y d 4 p p 2 i 0 displaystyle D lm el x y frac i 2 pi 4 g mu nu int frac e ip x y d 4 p p 2 i0 nbsp nbsp Ce nezavershena stattya z fiziki Vi mozhete dopomogti proyektu vipravivshi abo dopisavshi yiyi Posilannya Redaguvati Zagalnij viglyad matrichnih elementivLiteratura RedaguvatiYuhnovskij I R Osnovi kvantovoyi mehaniki K Libid 2002 392 s Bogolyubov N N Shirkov D V Vvedenie v teoriyu kvantovannyh polej M Nauka 1984 600 s Byorken Dzh D Drell S D Relyativistskaya kvantovaya teoriya M Nauka 1978 296 408 s Ventcel G Vvedenie v kvantovuyu teoriyu volnovyh polej M GITTL 1947 292 s Zi E Kvantovaya teoriya polya v dvuh slovah Izhevsk RHD 2009 632 s Icikson K Zyuber Zh B Kvantovaya teoriya polya M Mir 1984 448 400 s Peskin M Shryoder D Vvedenie v kvantovuyu teoriyu polya Izhevsk RHD 2001 784 s Rajder L Kvantovaya teoriya polya M Mir 1987 512 s Otrimano z https uk wikipedia org w index php title Propagator amp oldid 36979563
