Field theory in SO(2,3)* model of noncommutative gravity
Teorija polja u SO(2,3)* modelu nekomutativne gravitacije
Doktorand
Gočanin, DragoljubMentor
Radovanović, VojaČlanovi komisije
Dimitrijević-Ćirić, MarijaCvetković, Branislav
Metapodaci
Prikaz svih podataka o disertacijiSažetak
Arguably the greatest challenge of contemporary theoretical physics is to
understand the profound interplay between Quantum Mechanics (QM) and
the General Theory of Relativity (GR). To solve the conundrum of Quantum
Gravity" (QG) one has to transcend some deeply rooted assumptions on which
we are accustomed, in particular, at very short length scales we might have
to abandon the notion of a continuous space-time and the associated mathematical construct of a smooth manifold that describes it. Field theory on
noncommutative (NC) space-time is one distinguished approach to QG, and
the one that will be advocated in this thesis. NC field theory is based on the
method of quantization by deformation, originally developed for the purpose
of establishing phase-space quantum mechanics. One speaks of a deformation
of an object/structure whenever there is a family of similar objects/structures
of which the distortion" from the original, undeformed one can be somehow
parametrized. In physics, this... so-called deformation parameter is usually related to some fundamental constant of nature that measures the deviation
from the classical (i.e. undeformed) theory. To deform classical space-time,
one introduces an abstract algebra of NC coordinates, denoted by ^ xµ, that
satisfy some non-trivial commutation relations. The simplest case of noncommutativity is the so-called canonical (or θ-constant) noncommutativity,
[^ xµ; x^ν] = iθµν ∼ Λ2 NC, where θµν are components of a constant antisymmetric matrix, and ΛNC is a hypothetical length scale at which NC effects
become relevant. Instead of deforming abstract algebra of coordinates, one
can introduce space-time noncommutativity in the form of NC products of
functions (fields) on commutative space-time. These products are called star
products (?-products). In particular, canonical noncommutativity is effected
by the Moyal ?-product.
During the previous studies of the theory of NC gravity, it was found that
NC corrections to GR can be obtained by canonical deformation of anti-de
Sitter (AdS) gauge field theory. Starting with an action of the MacDowellMansouri type, invariant under SO(2; 3) gauge transformations, one obtains
the Einstein-Hilbert action with cosmological constant term, after choosing a
certain gauge. NC deformation is based on the Seiberg-Witten approach to
NC gauge field theory, and the first non-vanishing NC correction is quadratic
in θµν. This model also predicts a non-trivial NC deformation of Minkowski
space and offers an explanation for the apparent breaking of diffeomorphism
invariance in the NC theory. Namely, the structure of the NC-deformed Minkowski metric suggests that, by assuming canonical noncommutativity, we
implicitly choose a preferred frame of reference - the Fermi inertial frame...
Jedan od najve´cih izazova savremene teorijske fizike jeste usaglaˇsavanje
Opˇste teorije relativnosti (OTR) i Kvantne mehanike. Da bismo razreˇsili
problem kvantne gravitacije" neophodno je da prevazid¯emo neke duboko
ukorenjene pretpostavke na kojima se zasnivaju sve naˇse dosadaˇsnje teorije.
Jedna od njih je i pretpostavka da je struktura prostor-vremena kontinualna
na svim skalama i da shodno tome odgovara matematiˇckom konceptu glatke
mnogostrukosti. Teorija polja na nekomutativnom (NK) prostor-vremenu je
jedan dobro definisani pristup problemu kvantne gravitacije, i taj pristup ´ce
biti zastupljen u ovoj disertaciji. NK teorija polja poˇciva na metodu deformacione kvantizacije, originalno razvijenom radi zasnivanja kvantne mehanike
u faznom prostoru. O deformaciji nekog objekta/strukture govorimo onda
kada postoji familija srodnih objekata/struktura kod koje se odstupanje od
nedeformisanog originala moˇze na odred¯eni naˇcin paramatrizovati. U fizici
se ovaj takozvani parametar ...deformacije javlja u vidu neke fundamentalne
konstante prirode i predstavlja meru odstupanje od klasiˇcne" (tj. nedeformisane) teorije. Da bismo deformisali klasiˇcno prostor-vreme, uvodimo apstraktnu algebru nekomutativnih koordinata, u oznaci ^ xµ, koje zadovoljavaju
neke netrivijalne komutacione relacije. Najjednostavniji primer je takozvana
kanonska (ili θ-konstantna) nekomutativnost, [^ xµ; x^ν] = iθµν ∼ Λ2 NC, gde su
θµν komponente konstantne antisimetriˇcne matrice, a ΛNC hipotetiˇcka skala
duˇzine na kojoj efekti nekomutativnosti postaju znaˇcajni. Umesto deformisanja apstraktne algebre koordinata, nekomutativnost moˇzemo uvesti u vidu
nekomutativnih proizvoda funkcija (polja) obiˇcnih komutativnih koordinata.
Ovi proizvodi se nazivaju star-proizvodi (?-proizvodi). Konkretno, kanonskoj
nekomutativnosti odgovara Mojalov ?-proizvod.
Tokom prethodnih istraˇzivanja teorije NK gravitacije, ustanovljeno je da
se nekomutativna verzija OTR moˇze dobiti kanonskom deformacijom antide Siter (AdS) gradijentne teorije gravitacije. Predloˇzeno klasiˇcno dejstvo
Jang-Milsovog tipa, invarijantno na lokalne SO(2; 3) transformacije, se pri
odred¯enom kalibracionom uslovu svodi na standardno Ajnˇstajn-Hilbertovo
dejstvo sa kosmoloˇskom konstantom. NK deformacija je sprovodena slede´ci
Sajberg-Vitenov pristup NK teoriji gradijentnih polja, i ispostavlja se da
je prva nenulta NK korekcija kvadratna po θµν. Ovaj model takod¯e predvid¯a netrivijalnu deformaciju prostora Minkovskog i pruˇza objaˇsnjenje porekla
naruˇsenja opˇste kovarijantnosti koje je prisutno u NK teoriji. Naime, struktura NK-deformisane metrike Minkovskog ukazuje na to da, uvode´ci kanonsku
nekomutativnost, mi implicitno prelazimo u odred¯eni referentni sistem - onaj
koji odgovara Fermijevim inercijalnim koordinatama duˇz geodezika...
Fakultet:
Универзитет у Београду, Физички факултетDatum odbrane:
22-11-2019Projekti:
- Fizičke implikacije modifikovanog prostor-vremena (RS-MESTD-Basic Research (BR or ON)-171031)