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Properties of classical and quantum field theory on a curved noncommutative space

dc.contributor.advisorBurić, Maja
dc.contributor.otherRadovanović, Voja
dc.contributor.otherCvetković, Branislav
dc.creatorNenadović, Luka V.
dc.date.accessioned2018-05-24T09:50:08Z
dc.date.available2018-05-24T09:50:08Z
dc.date.available2020-07-03T09:50:54Z
dc.date.issued2017-07-13
dc.identifier.urihttp://eteze.bg.ac.rs/application/showtheses?thesesId=5781
dc.identifier.urihttp://nardus.mpn.gov.rs/handle/123456789/9453
dc.identifier.urihttps://fedorabg.bg.ac.rs/fedora/get/o:17648/bdef:Content/download
dc.identifier.urihttp://vbs.rs/scripts/cobiss?command=DISPLAY&base=70036&RID=50057999
dc.description.abstractPosle kratakog istorijskog prikaza razvoja nekomutativne geometrije i upoznavaa sa osnovnim osobinama i proble- mima kvantnih teorija po a formulisanih na nekomutativ- nim prostorima dat je uvod u tetradni formalizam u ne- komutativnoj diferencijalnoj geometriji. Razmotrili smo osnovne osobine ranije definisane modifikovane Hajzenber- gove algebre i opisali konstrukciju diferencijalne geome- trije na ovom nekomutativnom prostoru. Ovo je uraeno ko- rixeem tetradnog formalizma. Uvodna razmatraa za- vrxavamo navoeem prethodnog rezultata, gde je pokazana ekvivalencija Grose-Vulkenharovog modela i skalarne teo- rije na zakriv enom nekomutativnom prostoru. U nastavku predstav amo formulaciju i analizu Dirako- vog dejstva na modifikovanoj Hajzenbergovoj algebri. Kon- kretno, razmotrena je neminimalna interakcija sa pozadin- skim gravitacionim po em. Renormalizabilni model je do- bijen dimenzionom redukcijom na Hajzenbergovu algebru. Us- postav ena je ekvivalencija sa Vi-Turnerovim modelom koji je nekomutativna ekstenzija Gros-Nevoovog modela. Ovaj re- zultat je indikacija da je interakcija sa torzijom i kri- vinom neophodan (i dovo an) uslov za renormalizabilnost skalarnih i spinorskih teorija na zakriv enom nekomuta- tivnom prostoru. U posledem delu, predstavili smo rezultate raquna di- vergentnih kvantnih korekcija propagatora na nivou jedne pet e, za gradijentno U(1) po e na modifikovanom Hajzen- bergovom prostoru. Ova teorija je ranije formulisana i predstav a jednu ekstenziju Grose-Vulkenharovog modela za gradijentno po e. Model je qisto geometrijski, zasnovan na Jang-Milsovom dejstvu i BRST invarijantan. Nakon per- turbativne kvantizacije oko trivijalnog vakuuma, nalazimo divergentne nelokalne qlanove oblika 1 i 2 . Napo- sletku analiziramo znaqee ovih qlanova i mogunosti za popravku modelasr
dc.description.abstractIn the first part we shortly review the historical development of the noncommutative geometry. After presenting some of the main features and problems of the wide class of quantum field theories on noncommutative spaces, we give a brief introduction of the frame formalism in the noncommutative differential geometry. Introducing the earlier defined truncated Heisenbera algebra, we review the construction of differential geometric objects on it using the frame formalism. We complete the introduction by citing the previously shown equivalence of the Grosse-Wulkenhaar model with the scalar theory coupled to the curvature of the truncated Heisenberg space. Further, we present our construction and analysis of the Dirac action on the truncated Heisenberg algebra. In particular, the nonminimal couplings to the background gravitational field via torsion was considered. By the dimensional reduction to the Heisenberg algebra we obtained the renormalizable Vignes-Tourneret model which is an extension of the noncommutative Gross-Neveu model. This result indicates that, as on the commutative curved backgrounds, nonminimal couplings with torsion and curvature are necessary (and sufficient) for renormalisability of scalar and spinor theories on the curved noncommutative spaces. In the last part, we present our calculation of the divergent one-loop corrections to the propagators of the U(1) gauge theory on the truncated Heisenberg space, which is one of the gauge extensions of the Grosse-Wulkenhaar model. The model is purely geometric, based on the Yang-Mills action; the corresponding gauge-fixed theory is BRST invariant and has trivial classical vacuum. We quantize perturbatively around this vacuum and, along with the usual wave-function and mass renormalizations, we find divergent nonlocal terms of the and type. We discuss the meaning of these terms and possible improvements of the model.en
dc.formatapplication/pdf
dc.languagesr
dc.publisherУниверзитет у Београду, Физички факултетsr
dc.relationinfo:eu-repo/grantAgreement/MESTD/Basic Research (BR or ON)/171031/RS//
dc.rightsopenAccessen
dc.sourceУниверзитет у Београдуsr
dc.subjectnekomutativna geometrijasr
dc.subjectnoncommutative geometryen
dc.subjectquantum field theoryen
dc.subjectgauge theoryen
dc.subjectrenormalizationen
dc.subjectcurved spaceen
dc.subjectkvantna teorija po asr
dc.subjectgradijentna teorijasr
dc.subjectrenormalizacijasr
dc.subjectzakriv en pro- storsr
dc.titleОсобине класичне и квантне теорије поља на закривљеном некомутативном просторуsr
dc.title.alternativeProperties of classical and quantum field theory on a curved noncommutative spaceen
dc.typedoctoralThesis
dc.rights.licenseBY-NC-ND
dcterms.abstractБурић, Маја; Цветковић, Бранислав; Радовановић, Воја; Ненадовић, Лука В.; Osobine klasične i kvantne teorije polja na zakrivljenom nekomutativnom prostoru;
dc.identifier.fulltexthttp://nardus.mpn.gov.rs/bitstream/id/25138/IzvestajKomisije16879.pdf
dc.identifier.fulltexthttp://nardus.mpn.gov.rs/bitstream/id/25137/Disertacija.pdf


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