Jednadžbe renormalizacijske grupe i amplitude na razini dvije petlje

master's thesis

• Title (english): Renormalization group equations and amplitudes at two loop level
• Author: Marta Fatović
• Mentor: Amon Ilakovac (mentor)
• Committee member: Amon Ilakovac (predsjednik povjerenstva)
• Committee member: Matko Milin (član povjerenstva)
• Committee member: Krešimir Kumerički (član povjerenstva)
• Committee member: Nikola Poljak (član povjerenstva)
• Committee member: Davor Horvatić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); Zagreb
• Defense date and country: 2019-09-25, 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: renormalizacija; regularizacija; jednočestični ireducibini dijagrami; kvantna elektrodinamika; kvantna kromodinamika; Wardov identitet
• Keywords (english): renormalization; regularization; one particle irreducible diagram; quantum electrodynamics; quantum chromodynamics; Ward identity
• Language: croatian
• URN:NBN: urn:nbn:hr:217:414946
• Study programme: Title: 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 resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2020-01-08 09:13:18