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master's thesis
Jednadžbe renormalizacijske grupe i amplitude na razini dvije petlje
Zagreb: University of Zagreb, Faculty of Science, 2019. urn:nbn:hr:217:414946
Fatović, Marta
University of Zagreb
Faculty of Science
Department of Physics

Institutional repository: Repository of the Faculty of Science

Cite this document

Fatović, M. (2019). Jednadžbe renormalizacijske grupe i amplitude na razini dvije petlje (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:414946

Fatović, Marta. "Jednadžbe renormalizacijske grupe i amplitude na razini dvije petlje." Master's thesis, University of Zagreb, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:217:414946

Fatović, Marta. "Jednadžbe renormalizacijske grupe i amplitude na razini dvije petlje." Master's thesis, University of Zagreb, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:217:414946

Fatović, M. (2019). 'Jednadžbe renormalizacijske grupe i amplitude na razini dvije petlje', Master's thesis, University of Zagreb, Faculty of Science, accessed 19 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:414946

Fatović M. Jednadžbe renormalizacijske grupe i amplitude na razini dvije petlje [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2019 [cited 2024 December 19] Available at: https://urn.nsk.hr/urn:nbn:hr:217:414946

M. Fatović, "Jednadžbe renormalizacijske grupe i amplitude na razini dvije petlje", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:217:414946

Metadata
TitleJednadžbe renormalizacijske grupe i amplitude na razini dvije petlje
Title (english)Renormalization group equations and amplitudes at two loop level
AuthorMarta Fatović
MentorAmon Ilakovac (mentor)
Committee memberAmon Ilakovac (predsjednik povjerenstva)
Committee memberMatko Milin (član povjerenstva)
Committee memberKrešimir Kumerički (član povjerenstva)
Committee memberNikola Poljak (član povjerenstva)
Committee memberDavor Horvatić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Physics)
Zagreb
Defense date and country2019-09-25, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Physics
Abstract
Tema rada su renormalizacijske grupne jednadžbe za kvantnu elektrodinamiku i kvantnu kromodinamiku na razini dvije petlje. Pokazano je da je za izračun istih potrebno iz računa amplituda dijagrama izdvajati samo divergentne članove uz 1/ϵ i da to vrijedi za svaki red računa smetnje. Izračun divergentnih doprinosa za obje teorije je napravljen koristeći dimezionalnu regularizaciju koja čuva baždarnu invarijantnost. Račun se za razinu jedne petlje proveo ručno, a kasnije je provjeren i računalno, dok se za razinu dvije petlje proveo računalno koristeći pakete Wolfram Mathematice: FeynArts, FeynCalc, FeynRules, PaX i TARCER. Pri računu korekcije vrha za kvantnu elektrodinamiku na razini jedne petlje su zadržani i konačni doprinosi te se izračunao i anomalni magnetski moment. Pri računu beta funkcije za kvantnu kromodinamiku je pokazano da je jednostavnije koristiti metodu pozadinskog polja. Dobivene su beta funkcije za obje teorije te je dobivena ovisnost konstanti vezanja o energiji.
Abstract (english)
The subject of this thesis is calculation of renormalization group equations for quantum electrodynamics and quantum chromodynamics at two loop level. To obtain that, it was proven that it is necessary to extract only terms proportional to 1/ϵ from amplitude calculation and that it can be applied to any loop order. The calculation of divergent contributions was done using dimensional regularization which preserves gauge invariance. One loop corrections calculation was done by hand and later checked with Wolfram Mathematica packages: FeynArts, FeynCalc, FeynRules and PaX. For two loop level, the calculation was done with the same Wolfram Mathematica packages including another one: TARCER. While calculating the one loop vertex correction in quantum electrodynamics, the finite parts were also kept and the anomalous magnetic moment was calculated. It has been shown that it is much simpler to use the background field method for obtaining beta function in quantum chromodynamics. Beta functions for both theories were calculated and the coupling constant energy dependence was obtained.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:414946
Study programmeTitle: Physics; specializations in: Research
Course: Research
Study programme type: university
Study level: integrated undergraduate and graduate
Academic / professional title: magistar/magistra fizike (magistar/magistra fizike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2020-01-08 09:13:18