Mhedziso yeDirac. The Dirac equation. Quantum field theory

Ichi chinyorwa chinozvipira kubasa raPaul Dirac, uyo akaenzanisa zvakanyanya kubudirira kwemagetsi. Inotsanangura pfungwa dzinokosha dzinodiwa kuti unzwisise chinangwa chemuviri we equation, uyewo nzira dzokushandisa nayo.

Sayenzi uye masayendisiti

Munhu asingabatanidzi nesayenzi, anomiririra hurongwa hwekubudisa ruzivo nezvimwe zvemashiripiti. Uye masayendisiti, mumaonero evanhu vakadai, vanowanzoreva mutauro usinganzwisisiki uye vanyanyada kuzvikudza. Kuzivana nemutsvakurudzi, munhu ari kure nesayenzi anotaura kuti haana kunzwisisa physics kuchikoro. Nokudaro philistine fences pachayo kubva pane zivo yesayenzi uye anokumbira mutauriri wepamusoro akadzidza kutaura zviri nyore uye zvakajeka. Zvechokwadi, Paul Dirac, uyo kuenzanisa kwatinofungisisa, akagamuchirwa nenzira imwechete.

Elementary particles

Chimiro chepfungwa chagara chichikurudzira pfungwa dzinofungidzira. MuGirisi yekare, vanhu vakacherechedza kuti marwendo akareba, pamusoro pemakumbo akawanda akanga apfuura, akashandura maitiro nenguva, uye akaratidza kuti rutsoka rumwe kana shangu zvakatakura zviduku zviduku nenyaya yacho. Zvinhu izvi zvakasarudzwa kunzi "maatomu", kureva, "zvisingaoneki." Zita racho rinoramba riripo, asi zvakazoitika kuti maatomu ose uye zvinyorwa, izvo maatomu akanyorwa, zvinowanzobatanidzwa, zvakaoma. Izvi zvikamu zvinonzi "primaryary particles". Basa raDirac rakazvipira kune avo, kuenzanisa kwekuti hakuna kubvumira kutsanangura chete electron spin, asiwo kutora kuvapo kwe antielectron.

Corpuscular Wave Dualism

Kubudirira kwekutema mapepa ekupera kwezana remakore rechigumi nemapfumbamwe kwakatungamirira kwete kungozvigadzira, zvokudya nekatsi, asiwo kwakasimudzira mikana yesayenzi. Sezvo wakagamuchira shanduro yakadaro sechinhu chinokurumidza kufungidzira (yeuka, usati watanga kusvika kusvika pamaminitsi makumi matatu nemakumi matatu), masayendisiti akatanga kutora zvinyorwa zvakasiyana-siyana.

Dzidziso yezvigadzirwa zvezvinhu zvakange zviripo panguva iyoyo hazvingagoni kutsanangurira kana kufanotaura zvisingaoneki zviratidzo zvemakemikoro akaoma. Chokutanga, chiitiko chakakurumbira chaRutherford chakaratidza kuti atomu haisi iyo inonyatsooneka: mukati maro yaiva nheyo yakasimba yepamusoro iyo yaive ine magetsi asingakanganisi. Zvadaro kuwanikwa kwema radioactivity kwakaratidza kuti nucleus haisi monolith, asi ine ma proton neutron. Uye ipapo iyo inenge yakawanikwa panguva imwe chete yakawanda yehuwandu hwemagetsi, Heisenberg kusanzwisisika kwehutano uye kukanganisa kwenzvimbo yepakutanga zvikamu zvakakonzera kukurudzira nzira yakasiyana yakasayenzi yekudzidza nyika dzakapoteredza. Paiva nechikamu chitsva-physics yepakutanga zvikamu.

Nyaya huru pakutanga kwezana remakore rino rekuwanikwa kukuru mune zvishoma zvishoma ndiko kutsanangurwa kwekuvapo kwezvinhu zvepakutanga uye huwandu uye zvivako zvehuyu.

Einstein akaratidza kuti kunyange photon isina simba ine mashoma, sezvo ichiita kuti munhu ave nechido chakasimba kune muviri wakasimba, unowira (chinoshamisa chekudzivirira kwechiedza). Panguva imwecheteyo, kuedza kwakawanda kwekupararira kwema electrons pane slits kwakataura zvakanyanya pamusoro pekuvapo kwekusiyana uye kupindira mukati mavo, izvi zvinoshamisa chete kumhepo. Pakupedzisira, ndaifanira kubvuma: zvinyorwa zvepakutanga zvose zviri chinhu chakashambadza uye chimiro. Iko ndiko, masero e, anoti, electron "inogadzirwa" mu packet ye simba ine wave yeimba. Iyi nheyo yegadzirisiti-wave yehutatu yakaita kuti zvive nyore kutsanangura kutanga kwekuti sei electronsi isingawi pasi, uye nokuda kwezvikonzero zvipi zvinotenderera muatomu, uye kuchinja pakati pavo kwakangoerekana. Izvi zvinoshanduka zvinoumba zvakasiyana-siyana kune chero zvinhu. Uyezve, fisikiti yepakutanga zvikamu inofanira kutsanangura zvinhu zvezvikamu zvega, pamwe nekubatana kwavo.

Mhepo inoshandiswa uye inowanzo nhamba

Erwin Schrödinger akaita zvishamiso zvinoshamisa uye zvisingazwisisiki (pane nheyo yake gare gare, Paul Dirac akavaka dzidziso yake). Akaratidza kuti humwe hwehupi hupi hwepurasitiki, semuenzaniso, we electron, hunorondedzerwa nemhepo inoshandiswa ψ. Nayo pachayo, hazvireve chimwe chinhu, asi rutivi rwayo runoratidza hutano hwekuwana electron munzvimbo inenge iri munzvimbo. Mamiriro ezvinhu epakutanga muatomu (kana imwe sarudzo) inotsanangurwa nhamba dzenhamba ina. Ichi ndicho chikuru (n), chibvumirano (l), magnetic (m) uye spin (m _s ) nhamba. Zvinoratidza zvinhu zvepurasitiki yepakutanga. Sekufananidza, unogona kuuya nehairi yamafuta. Maitiro aro - uremu, hukuru, ruvara uye mafuta. Zvisinei, iyo inorondedzera zvinyorwa zvepakutanga haigoni kunzwisiswa intuitively, inofanira kuonekwa kuburikidza nemashoko ekunyora. Basa reDirac, iro kuenzanisira ndiro chinotarisa munyaya ino, rinopihwa kune yekupedzisira, nhamba yepiniti.

Spin

Usati waenderera mberi kune iyo equation, zvakakosha kutsanangura kuti nhamba yep spin m _isani . Inoratidza nguva yepakati yekumhanya kwe electron uye zvimwe zvikamu zvepakutanga. Nhamba iyi nguva dzose inofadza uye inogona kutora nhamba yakakwana, zero kana hafu-integer kukosha (ye electron m _s = 1/2). Tsvina isvector value uye iyo chete inotsanangura maitiro e electron. Quantum field theory inoisa spin pachikonzero chekushandurana kwekushandura, uko kusina analogog inowanzo intuitive mechanics. Iyo nhamba yefinini inoratidza kuti vector inofanira kudzoka sei kusvika kumamiriro ekutanga. Muenzaniso ndewetiwo bhoti-peni yakawanda (chikamu chekunyorera chirevo chakanaka chevector). Kuti zviite kuti zviuye kune zvayo zvepakutanga, zvinofanira kunge zvichishandurudzwa madigiri 360. Iyi mamiriro akafanana nekapine yakaenzana ne1. Nokuti shure kwe2 1/2, kufanana ne electron, kutenderera kunofanira kuva zviyero 720. Nokudaro, kunze kwemasvomhu yemasikirwo, munhu anofanira kunge akavaka mafungiro ekudenga kuitira kuti anzwisise ichi chivako. Zvishoma zvishoma pamusoro pedu takataura pamusoro pekushanda kwemhepo. Ndiyo "mutevedzeri mukuru" weSchrödinger equation, iyo inotsanangura nyika nechinzvimbo chekutanga chetatu. Asi hukama uhwu muhupenyu hwepakutanga hwakagadzirirwa zvikamu zvisingatauri. Tinogona kutsanangura mamiriro e electron chete kana tikaita shanduro yeScrodinger equation, yakaitwa mubasa raDirac.

Mabhononi nevarimi

Fermion inongova nehafu-inobatsira spin kukosha. Fermions inowanikwa mumasikirwo (semuenzaniso, maatomu) maererano nemutemo wechiPauli: munharaunda imwe neimwe haifaniri kunge yakapfuura imwechete. Nokudaro, muatomu, electron imwe neimwe yakasiyana zvakasiyana nedzimwe dzose (imwe nhamba yechipumusi ine tsanangudzo yakasiyana). Quantum field theory inotsanangura imwe nyaya - mabasa. Vane sarudzo yose uye vose vanogona kunge vari mune imwechete panguva imwe chete. Kuziva kwechiitiko ichi kunonzi Bose condensation. Pasinei netsika yakanyatsorongeka yekuwana iyo, izvi zvaive zvichiitwa muna 1995 chete.

The Dirac equation

Sezvatareva pamusoro apa, Paul Dirac akawana kuenzanisa kwemalasi yeklasi ye electron. Iyo inotsanangurawo zvinyorwa zvezvimwe zviyo. Icho chirevo chemuviri chehukama chacho chakaoma uye chakawanda, uye dzakawanda zvinganzwisisika zvinotevera kubva pane zvayo. Chimiro che equation ndechekuti:

- (mc ² α ₀ + c Σ a _k p _k {k = 0-3}) ψ (x, t) = i ħ {∂ ψ / ∂ t (x, t)},

Apo m ishamba ye fermion (kunyanya, electron), c ndiyo inokurumidza kwechiedza, p _k ndiyo inofamba nhatu yezvikamu zvinowedzera (pamwe ne x, y, z axes), ħ ndiyo nguva yakagadziriswa Planck, x uye t ndiyo mitsara mitatu yepakati (inofanana ne X , Y, Z) uye nguva, zvichienderana, uye ψ (x, t) ndiyo yechina-inhengo yakaoma wave wave, α _k (k = 0, 1, 2, 3) -Matri matrices. Izvozvo ndezvevashandisi vakasiyana-siyana vanoita basa rinoshandiswa uye nzvimbo yacho. Iyi shanduro yakanyanya kuoma. Kuti tinzwisise kunyange zvikamu zvayo, tinofanira kunzwisisa zvitsanangudzo zvekutengesa kwevhisiyumu. Uyewo, munhu anofanira kunge ane ruzivo rwemasvomhu runoshamisa kuitira kuti atadze kuziva kuti vector, matrix uye operator chii. Kune unyanzvi, chimiro che equation chichati kunyange kupfuura zvinopfuura zvayo. Munhu ane ruzivo rwefizikiki yenyukireya uye anozivikanwa nemagetsi emagetsi achanzwisisa kukosha kwehukama uhwu. Zvisinei, tinofanira kubvuma kuti dirac neSchrödinger equations ndeyekutanga kwekutanga kwemasvomhu yekutsanangurwa kwezviitiko zvinowanikwa munyika yenhamba yakawanda. Nyanzvi dze physics dzinofanirwa kuzvipira kuzvikoro zvepakutanga uye kushamwaridzana kwavo, dzinofanira kunzwisisa chinangwa chehukama uhwu mugore rekutanga rechipiri chechikoro. Asi iyi yesayenzi inonakidza, uye iri munharaunda iyi iyo munhu anogona kuita kubudirira kana kupfuurira zita rake, kuronga kuenzanisa kwake, kushandurwa kana pfuma.

Icho chinoreva chimiro che equation

Sezvatakapikira, tinotaurira kuti chii chinoenderana neDirac equation ye electron ine. Chokutanga, kubva paukama huno hunova pachena kuti electron spin is ½. Chechipiri, maererano nean equation, electron ine maginetic yake nguva. Izvo zvakaenzana neBohr magneton (unit of the elementary magnetic moment). Asi mhedzisiro inonyanya kukosha yekuwana hukama uhwu huri munharaunda isina kukodzera α _k . Kubviswa kweDirac equation kubva kuStranding equation yakatora nguva yakareba. Pakutanga Dirac akafunga kuti avo vanofambisa vanopesana nechiyero. Achishandisa maitiro akasiyana-siyana emasvomhu, akaedza kuvadzivisa kubva ku-equation, asi haana kubudirira. Somugumisiro, dirac equation yehurukuro yakasununguka inoshandisa vana vanoshanda α. Mumwe nomumwe wavo ane matrix [4x4]. Miri mbiri inofananidzwa nehuwandu hwemafuta e electron, anoratidza kuti kune nzvimbo mbiri dzaro. Mamwe mairi maviri anopa mhinduro yehuipi hwakaipa hwechikamu. Ruzivo rwakajeka mufizikiki runopa munhu mukana wekugumisa kuti izvi hazvibviri muchokwadi. Asi semugumisiro wekuedza kwakawanikwa kuti matrices maviri ekupedzisira ndiwo magadzirirwo ehutundu huripo hwakatarisana ne electron-antielectron. Sezvakaita electron, positron (sezvavakadana ichi chikamu) ine uwandu, asi mutemo wayo wakanaka.

Positron

Sezvo zvaiwanzoitika panguva yekuwana yakawanda, Dirac pakutanga haana kutenda zvaanofunga. Haana kuedza kutaura pachena pachena kufanotaura kwechinhu chitsva. Ichokwadi, munyaya dzakawanda uye pamasangano akasiyana-siyana ehurukuro, maasayendisiti akasimbisa kuvepo kwekuvapo kwayo, kunyange zvazvo asina kuitora. Asi nguva pfupi mushure mekubudiswa kweukama hunozivikanwa, positron yakawanikwa muzhizha ye cosmic. Nokudaro, huripo hwacho hwakasimbiswa. Iko positron ndiyo yekutanga yeantimatter inowanikwa nevanhu. A positron inoberekwa semumwe wemapatya maviri (rimwe rimwe mapatya ndiro electron) mukubatana kwemasimba ane simba zvakanyanya nenyaya yekanyaya mune imwe simba remagetsi. Hatingatauri maverengi (muverengi anofarira achawana ruzivo rwemunhu oga). Zvisinei, inofanira kusimbiswa kuti tiri kutaura pamusoro pezvikero zvepakati. Kuburikidza kwekuputika kwe-supernovas uye kukoromoka kwemapoka enyeredzi kunokwanisa kubudisa photons yemasimba anodiwa. Izvo zvinowanikwawo mune imwe nzvimbo mumoyo weredzi dzinopisa, kusanganisira Sun. Asi vanhu vanogara vachiedza ivo pachavo kubatsirwa. Annihilation yenyaya ne antimatter inopa simba rakawanda. Kuti zvibvise izvi uye zvitange kuti zvibatsire humunhu (semuenzaniso, injini dze interstellar liners pakuparadzwa dzinenge dzichibudirira), vanhu vakadzidza kuita mapurotoni mu laboratori.

Kunyanya, hurukuro dzakawanda (dzakadai sedhironi ye hadron) dzinogona kugadzira electron-positron pairs. Pamberi pacho, zvakanziwo kuti pane zvisizvo zvekutanga zvinoparadzanisa (kune mamwe akawanda kunze kwe electron), asiwo antimatter yose. Kunyange chiduku chiduku chekristal chero ipi zvayo kubva kune antimatter yaizopa simba kunyika yose (zvichida superman kryptonite yaiva antimatter?).

Asi tarisai, kusikwa kwe antimatter yakaremara kudarika hydrogen nuclei muzvinhu zvakatarisika zvisina kunyorwa. Zvisinei, kana muverengi achifunga kuti kushamwaridzana kwechinhu (regai tisimbise, iyo nyaya, uye kwete iyo electron mumwe nomumwe) ne positron inoguma pakarepo nekuparadzwa, saka inokanganisa. Apo positron inoderedzwa nokukurumidza, imwe yakasanganiswa electron-positron pamwe chete, iyo inonzi positronium, inowanikwa mune zvimwe zvinodhaka zvisina unzero. Izvi zvakagadzirisa zvimwe zvinhu zveatomu uye zvinokwanisa kunyange kupinda mune maitiro emakemikari. Asi izvi zvisinganzwisisiki hazvirevi kwenguva refu uye zvino zvichiri kuparadza nekubudiswa kwezviviri, uye mune dzimwe nguva, matatu gamma quanta.

Kukanganiswa kwe equation

Pasinei nokuti icho chikonzero nekuda kwehukama ichi antielectron uye antimatter yakaonekwa, ine dambudziko rakakura. Nhoroondo yeiyo equation uye mufananidzo wakavakirwa pazvikonzero zvayo haikwanisi kufanotaura kuti mapoka anozvarwa sei uye anoparadzwa. Iko rudzi rwekunyepedzera kwenyika yenyika: nheyo iyo yakafanotaura kuberekwa kwenyaya-antimatter pairi haikwanise kunyatsotsanangura izvi. Uku kushayikwa kwacho kwakabviswa muhuwandu hwemashoko. Nokutaura kuverenga kwemasimi, iyo muenzaniso inotsanangura kushamwaridzana kwavo, kusanganisira kusikwa nekuparadzwa kwezvinhu zvepakutanga. Ne "quantum field field" munyaya iyi inoreva nguva yakakwana. Iyi ndiyo munda wefizikiki inodzidza maitiro ekuwanda kweminda.

The Dirac equation mumagariro e-cylindrical

Kutanga, ngatitaurei kuti cylindrical coordinate system chii. Panzvimbo yeiyo inowanzogara mitatu inopindirana, inowona, nzvimbo uye nzvimbo yakakwirira inoshandiswa kutsanangura nzvimbo chaiyo yenzvimbo munzvimbo. Izvo zvakafanana ne polar coordinate system mundiza, chete yechitatu nharaunda - kureba kunowedzerwa. Iyi nzira yakagadzikana kana inofanirwa kurondedzera kana kutsvaga imwe nzvimbo yakasiyana-siyana maererano neimwe yenharo. Nekuwanda kwemajini, ichi chinhu chakakosha uye chakanaka chinokubvumira kuti uwedzere zvakanyanya kuwanda kwemafomu uye nhamba yekuverenga. Ichi chigumisiro chesisimymmetry yegore re electron muatomu. Iyo Dirac equation mumagariro e-cylindrical inogadziriswa zvakasiyana zvakasiyana pane mune tsika yechimiro, uye dzimwe nguva inopa migumisiro isingatarisirwi. Semuenzaniso, mamwe matambudziko akashandiswa pakugadzirisa maitiro ezvinyorwa zvepakutanga (kazhinji magetsi) mumunda wakagadziriswa akagadziriswa nekushandura maitiro eedation kusvika kumagariro ekugadzirisa.

Kushandiswa kweiyo equation pakugadzirisa chimiro chezvikamu

Iko kuenzanisa kunotsanangura zvidimbu zvakajeka: izvo zvisingaiti kunyange zviduku zviduku. Sayenzi yemazuva ano inokwanisa kuenzanisa magnetic nguva nekwaniso yakakwana yakakwana. Nokudaro, kukanganisa pakati pehuwandu hunotaridzwa neDirac equation uye kuedza kwekuyera magnetic moment kunoratidzira zvakananga chimiro chakaoma chechidimbu. Tinoyeuka kuti iyi equation inoshandiswa kune fermions, spin yavo inenge hafu-inokosha. Kushandisa iyi equation, sangano rakaoma reprotoni uye neutron rakasimbiswa. Chimwe nechimwe chazvo chinosanganisira kunyange zviduku zviduku, zvinonzi quarks. Munda wegluon unochengetedza quarks pamwe chete, kwete kuvabvumira kuti vashanduke. Pane chirevo chekuti quarks haisi iyo yepakutanga zvikamu zvepasi redu. Asi kana vanhu vasina simba rakakwana rekugadzirisa.