Towards a field theory on quantized space

Otvoreno pitanje u modernoj teorijskoj fizici predstavlja ujedinjenje kvantne mehanike i gravitacije unutar istog matematičkog formalizma. Mogući pristup problemu je da pretpostavimo da je na malim skalama prostorvrijeme kvantizirano te pokušamo konstruirati teoriju polja na takvoj strukturi. U ovom radu konstruiramo kvantizirane, odnosno nekomutativne varijante homogenih prostora, uzimajući u obzir zahtjev, po uzoru na princip korespondancije u kvantnoj mehanici, da postoji odgovarajući limes u kojem se nekomutativni prostor reducira na glatku mnogostrukost. Konkretna konstrukcija nekomutativnih analogona homogenih prostora ilustrirana je na primjerima kvantne mehanike i kvantizirane sfere. U kontekstu kvantizirane varijante klasične sfere uvodimo dinamičke nekomutativne prostore, baždarnu teoriju polja te osnovne koncepte kvantne teorije polja na nekomutativnim prostorima.An open question in modern theoretical physics is the union of quantum mechanics and gravity within the same mathematical framework. One approach to this problem is that we assume that spacetime is quantized on small scales and attempt to construct a field theory on such a structure. In this dissertation we construct quantized, that is, noncommutative analogues of homogeneous spaces, taking into consideration the request that, similarly to the correspondence principle in quantum mechanics, there is a corresponding limit in which the noncommutative space reduces to a smooth manifold. An explicit construction of noncommutative analogues of homogeneous spaces is illustrated on the examples of quantum mechanics and the quantized sphere. In the context of a quantized version of the classical sphere, we introduce dynamical noncommutative spaces, gauge field theory and basic concepts of quantum field theory on noncommutative spaces

Seasonal variability of the flavonoids contents of Laurus nobilis L. (Lauraceae) from Lovran

U okviru ovoga diplomskog rada provedena je kvantitativna analiza flavonoida lista lovora (Laurus nobilis L., Lauraceae) s područja Lovrana, kroz razdoblje od svibnja 2015. do travnja 2016. godine, a u svrhu praćenja sezonske varijabilnosti sadržaja tih biološki aktivnih polifenolnih tvari. Udio flavonoida lovora, izražen kao kvercetin, određen je spektrofotometrijski na 421 nm (maksimum apsorpcije), odnosno na 425 nm (prema izvornoj metodi). Sadržaj ukupnih flavonoida u listovima lovora (apsorbancija na 421 nm) kretao se u rasponu od 0,26% (ožujak i travanj 2016.) do 0,74% (kolovoz 2015.), odnosno u rasponu od 0,23% (ožujak i travanj 2016.) do 0,71% (kolovoz 2015.) (apsorbancija na 425 nm). Provedena kvantitativna analiza predstavlja doprinos znanstvenom istraživanju lovora i upotpunjuje dosadašnje spoznaje o sadržaju polifenolnih sastavnica, posebice u pogledu udjela flavonoidnih tvari i njihove sezonske varijabilnosti, što može pomoći u procjeni fitoterapijskog potencijala te vrste Laurus nobilis L.In this work, quantitative analysis of flavonoids in leaves of Laurus nobilis L. (Lauraceae) from Lovran was carried out. The samples of laurel leaves were collected during one year period (from May 2015 to April 2016) with the intention of determining the seasonal variability of the flavonoid contents. Quantitative analysis of flavonoids was carried out using the spectrophotometric method. The contents of analyzed compounds varied in laurel leaves from 0,26% (March and April 2016) to 0,74% (August 2015) (421 nm, max. abs.), and from 0,23% (December 2015) to 0,71% (August 2015) (425 nm, according to method). Conducted quantitative analysis is a contribution to the scientific study of polyphenols of Laurus nobilis L. and completes the existing knowledge about phytotherapeutic potential of laurel, especially in relation to the content and seasonal variability of flavonoid substances

Towards a field theory on quantized space

Otvoreno pitanje u modernoj teorijskoj fizici predstavlja ujedinjenje kvantne mehanike i gravitacije unutar istog matematičkog formalizma. Mogući pristup problemu je da pretpostavimo da je na malim skalama prostorvrijeme kvantizirano te pokušamo konstruirati teoriju polja na takvoj strukturi. U ovom radu konstruiramo kvantizirane, odnosno nekomutativne varijante homogenih prostora, uzimajući u obzir zahtjev, po uzoru na princip korespondancije u kvantnoj mehanici, da postoji odgovarajući limes u kojem se nekomutativni prostor reducira na glatku mnogostrukost. Konkretna konstrukcija nekomutativnih analogona homogenih prostora ilustrirana je na primjerima kvantne mehanike i kvantizirane sfere. U kontekstu kvantizirane varijante klasične sfere uvodimo dinamičke nekomutativne prostore, baždarnu teoriju polja te osnovne koncepte kvantne teorije polja na nekomutativnim prostorima.An open question in modern theoretical physics is the union of quantum mechanics and gravity within the same mathematical framework. One approach to this problem is that we assume that spacetime is quantized on small scales and attempt to construct a field theory on such a structure. In this dissertation we construct quantized, that is, noncommutative analogues of homogeneous spaces, taking into consideration the request that, similarly to the correspondence principle in quantum mechanics, there is a corresponding limit in which the noncommutative space reduces to a smooth manifold. An explicit construction of noncommutative analogues of homogeneous spaces is illustrated on the examples of quantum mechanics and the quantized sphere. In the context of a quantized version of the classical sphere, we introduce dynamical noncommutative spaces, gauge field theory and basic concepts of quantum field theory on noncommutative spaces

NLO corrections to the deeply virtual meson production revisited: impact on the extraction of generalized parton distributions

We revisit the next-to-leading order (NLO) perturbative QCD corrections for the deeply virtual meson production (DVMP) process, exploring its phenomenology both in isolation and in a multichannel fit combined with deeply virtual Compton scattering (DVCS). Our approach involves the conformal partial wave (CPaW) formalism, which allows for the straightforward inclusion of higher-order contributions and evolutionary effects. Our findings indicate that a description of the longitudinal component of the vector meson DVMP cross-section at high energies is achievable only at NLO within the standard collinear approach. Furthermore, we demonstrate a simultaneous description of DIS, DVCS, and DVMP processes, providing insights into the proton structure described at NLO by unique universal generalized parton distribution (GPD) functions.Comment: 36 pages, 13 figure

Oslikavanje trodimenzijske kvarkovsko-gluonske strukture protona analizom duboko virtualnih raspršenja elektrona

The study of the structure of the proton has been an ongoing effort ever since its first experimental discovery in 1917 by Rutherford. As experimental methods progressed, and the properties of the proton, such as its mass, spin and charge, were uncovered, the question of its underlying structure arose. Experiments conducted in 1969 at SLAC undoubtedly confirmed the fact that the proton is not an elementary particle, but that it consists of smaller particles, which we now recognize as quarks and gluons. From that point on, physicists tried to understand how exactly the interplay of quarks and gluons inside the proton gives rise to its properties. One of the ways we can experimentally study the proton is through hard exclusive processes, such as deeply virtual Compton scattering (DVCS) and deeply virtual meson production (DVMP), which give access to a class of functions called generalized parton distributions (GPDs). GPDs describe the three dimensional structure of the proton, and they are a potential solution to the proton spin puzzle. It is currently not possible to extract GPDs from measurements directly, since they are convoluted with hard scattering amplitudes inside cross sections, and deconvolution is in itself an ill-posed problem. These functions are also not possible to calculate from first principles due to the non-perturbative nature of QCD, so we rely on modeling and machine learning methods in order to extract them from measurements. In this work we present recent results on the extraction of GPDs and relevant form factors from DVCS and DVMP data. Using the more recent proton DVCS data, we extract the set of leading Compton form factors (CFFs) with uncertainties and, by adding neutron DVCS data, we separate the contributions of up and down quarks to the CFF H. We make simultaneous fits to high energy deep inelastic scattering, DVCS and DVMP data at low x and study the impact of next-to-leading order (NLO) corrections, as well as the possibility of a unique description of these processes with twist-2 GPDs. We demonstrate a sizeable impact of NLO corrections and that extraction of unique GPDs becomes possible at NLO.Proučavanje strukture protona započelo je prije više od 100 godina. Od prvog Rutherfordovog otkrića 1917., kada se smatralo da je proton točkasta čestica, preko razumijevanja da ipak ima podstrukturu, pa do mjerenja dubokog neelastičnog raspršenja 1969. na SLAC-u, gdje se potvrdilo da je ta podstruktura netrivijalna, proučavanje protona, osnovne građevne jedinice svemira, predstavlja uzbudljivo i rastuće područje u fizici. U ovom radu bavit ćemo se strukturom protona kroz proučavanje generaliziranih partonskih distribucija (GPD-ova). GPD-ovi predstavljaju interesantno područje istraživanja utoliko što objašnjavaju trodimenzijsku raspodjelu kvarkova i gluona u protonu, daju rješenje zagonetke protonskog spina, kao i mnoga druga svojstva. Povijesni tijek eksperimentalnog ispitivanja svojstava protona krenuo je s elastičnim raspršenjem. Nabijena proba, tipično elektron, sudara se s protonom i raspršuje se na njemu. Elektromagnetska interakcija probe s protonom, koja se prenosi virtualnim fotonima, daje nam uvid u raspodjelu električnog naboja protona. Već se ovakvim eksperimentom može vidjeti da proton nije točkasta čestica, nego da posjeduje prostornu protežnost. Povećavanjem energije elektrona dolazimo u režim neelastičnog raspršenja, gdje struktura protona apsorbira dio energije elektrona. Elektromagnetska svojstva protona razotkrivena ovim eksperimentom ne mogu doći od elementarne čestice, čime se nazire netrivijalna podstruktura protona

COMMON AGRICULTURAL POLICY OF THE EUROPEAN UNION

Europska unija je po svom pravnom uređenju monetarna unija, tj. unija dvije ili više država koje postaju članice unije. Neke od glavnih karakteristika takve unije su da države članice moraju imati zajedničku valutu i središnju banku. Također je jedna od važnih karakteristika da monetarna unija teži centralizaciji vođenja politike, odnosno nijedna država članica koja je dio Unije, ne može voditi samostalnu politiku. Jedna od zajedničkih politika Europske Unije je zajednička poljoprivredna politika Europske unije. Ugovor kojim je osnovana ova politika je potpisan 25. ožujka 1957. u Rimu te se zbog toga koristi naziv za ovaj Ugovor – Rimski ugovor (Treaty establishing the European Economic Community, ECC Treaty). S ovim ugovorom je uspostavljena zajednica tada šest europskih država radi razvijanja zajedničkog tržišta, carinske unije te radi ostvarivanja zajedničkih politika. Najveći dio ukupnog europskog godišnjeg proračuna se koristi upravo za provođenje ove politike jer je 80% površine tla unije poljoprivredno područje, a to podrazumijeva tla, šume, mora, rijeke itd. Europska Komisija odlučuje u skladu sa prijedlozima država članica koliki će dio proračuna dobiti svaka država članica za provedbu plana ZPP-a, a planovi se uglavnom baziraju na tome kako modernizirati poljoprivredu, što treba promijeniti u radu poljoprivrede zbog klimatskih promjena, na koje načine postići kontrolu poljoprivrednih poduzeća, kako privući mlade da se počnu baviti poljoprivredom. Dva najvažnija fonda za provedbu zajedničke poljoprivredne politike su EAGF (Europski fond za jamsta u poljoprivredi, European Agricultural Guarantee Fund) i EAFRD (Europski poljoprivredni fond za ruralni razvoj, European Agricultural Fund for Rural Development).In its legal form, the European Union is a monetary union, ie a union of two or more states that become members of the union. One of the main features of such a union are that Member States must have a common currency and a Central Bank. Another important characteristic is that a monetary union tends to centralize policy-making, that is, no Member State that is part of the Union can pursue an independent policy. One of the common policies of the European Union is the common agricultural policy. The Treaty establishing this policy was signed in Rome on 25th March 1957 and is therefore referred to as the Rome Treatyor the Treaty establishing the European Economic Community (ECC Treaty). With this treaty, a community of then six European countries was established to develop a common market, a customs union and to pursue common policies. The largest part of the total European annual budget is used precisely to implement this policy, since 80% of the Union's surface is an agricultural area, which includes land, forests, seas, rivers, etc. The European Commission decides in accordance with the Member States' proposals how much of the budget will be received by each Member State to implement the CAP, and the plans are mainly based on how to modernize agriculture, what needs to be changed in agriculture due to climate change, how to achieve control of agricultural enterprises, how to attract young people to start farming. The two most important funds for implementing the common agricultural policy are the European Agricultural Guarantee Fund (EAGF) and the European Agricultural Fund for Rural Development (EAFRD)

Towards a field theory on quantized space

Otvoreno pitanje u modernoj teorijskoj fizici predstavlja ujedinjenje kvantne mehanike i gravitacije unutar istog matematičkog formalizma. Mogući pristup problemu je da pretpostavimo da je na malim skalama prostorvrijeme kvantizirano te pokušamo konstruirati teoriju polja na takvoj strukturi. U ovom radu konstruiramo kvantizirane, odnosno nekomutativne varijante homogenih prostora, uzimajući u obzir zahtjev, po uzoru na princip korespondancije u kvantnoj mehanici, da postoji odgovarajući limes u kojem se nekomutativni prostor reducira na glatku mnogostrukost. Konkretna konstrukcija nekomutativnih analogona homogenih prostora ilustrirana je na primjerima kvantne mehanike i kvantizirane sfere. U kontekstu kvantizirane varijante klasične sfere uvodimo dinamičke nekomutativne prostore, baždarnu teoriju polja te osnovne koncepte kvantne teorije polja na nekomutativnim prostorima.An open question in modern theoretical physics is the union of quantum mechanics and gravity within the same mathematical framework. One approach to this problem is that we assume that spacetime is quantized on small scales and attempt to construct a field theory on such a structure. In this dissertation we construct quantized, that is, noncommutative analogues of homogeneous spaces, taking into consideration the request that, similarly to the correspondence principle in quantum mechanics, there is a corresponding limit in which the noncommutative space reduces to a smooth manifold. An explicit construction of noncommutative analogues of homogeneous spaces is illustrated on the examples of quantum mechanics and the quantized sphere. In the context of a quantized version of the classical sphere, we introduce dynamical noncommutative spaces, gauge field theory and basic concepts of quantum field theory on noncommutative spaces

Separation of Quark Flavors Using Deeply Virtual Compton Scattering Data

Using the available data on deeply virtual Compton scattering (DVCS) off protons and utilizing neural networks enhanced by the dispersion relation constraint, we determine six out of eight leading Compton form factors in the valence quark kinematic region. Furthermore, adding recent data on DVCS off neutrons, we separate contributions of up and down quarks to the dominant form factor, thus paving the way towards a three-dimensional picture of the nucleon

Separation of Quark Flavors Using Deeply Virtual Compton Scattering Data

Using the available data on deeply virtual Compton scattering (DVCS) off protons and utilizing neural networks enhanced by the dispersion relation constraint, we determine six out of eight leading Compton form factors in the valence quark kinematic region. Furthermore, adding recent data on DVCS off neutrons, we separate contributions of up and down quarks to the dominant form factor, thus paving the way towards a three-dimensional picture of the nucleon