Računanje jednopetljenih Feynmanovih dijagrama direktnom numeričkom metodom

doctoral thesis

• Title (english): Direct numerical calculation of one-loop Feynman diagrams
• Author: Bruno Klajn
• Mentor: Goran Duplančić (mentor)
• Committee member: Amon Ilakovac (predsjednik povjerenstva)
• Committee member: Goran Duplančić (član povjerenstva)
• Committee member: Mirko Planinić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); Zagreb
• Defense date and country: 2016-08-07, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics
• Universal decimal classification (UDC): 53 - Physics

Abstract

U ovom je doktorskom radu izložena nova, potpuno numerička metoda izračuna jednopetljenih Feynmanovih amplituda. Metoda se temelji na dvjema postojećim metodama za numerički izračun jednopetljenih Feynmanovih dijagrama. U jednoj se od tih metoda numerička stabilnost postiže deformacijom integracijske krivulje u kompleksnu ravninu, dok se u drugoj metodi integrabilni singulariteti regula- riziraju Feynmanovim ∈ parametrom, te se fizikalna vrijednost dijagrama dobije ekstrapolacijom ∈ → 0. Za razliku od ovih metoda, koje su namijenjene izračunu pojedinih dijagrama, novom se metodom računa kompletna amplituda, dana kao suma dijagrama, odjednom. Nakon što se amplituda rastavi na dva, tzv. UV i IR, doprinosa, UV doprinos se računa deformacijom integracijske krivulje, dok se IR doprinos računa s konačnim ∈, te naknadno ekstrapolira prema ∈ → 0. Računanjem cjelokupne amplitude odjednom, dobiva se na ekonomičnosti i stabilnosti samog računa, te se eliminira potreba za regularizacijom pojedinih dijagrama u slučaju konačnih amplituda. Metoda je implementirana u programskom jeziku Wolfram Mathematica i primjenjena na slučaj raspršenja u skalarnoj teoriji i kvantnoj elektrodinamici.

Abstract (english)

Presented in this thesis is a new, completely numerical approach to one-loop Feynman amplitudes. The method is based upon two existing methods of numerical calculation of one-loop Feynman diagrams. In one of these methods, the numerical integration is performed by a contour deformation into a complex plane, while the other method regularizes the integrable singularities by keeping the Feynman ∈ parameter _nite and then calculates the physical value of the diagram by extrapolation ∈ ! 0. Contrary to these methods, which are designed to calculate individual diagrams, the new method calculates the complete amplitude, given as a sum of diagrams, at once. After separating the amplitude into two contributi- ons, named UV and IR, the UV contribution is integrated via contur deformation, while the IR contribution is calculated using finite ∈ parameter and subsequently extrapolated for the value ∈ ! 0. Calculating the complete amplitude at once is more economical and numerically stable approach and it elliminates the need for diagram regularization whenever the complete amplitude is finite. The method is implemented in the Wolfram Mathematica language and applied to calculation of scattering amplitudes in scalar theory and quantum electrodynamics.

• Keywords: kvantna teorija polja; jednopetljeni Feynmanovi dijagrami; amplituda raspršenja
• Keywords (english): quantum field theory; scattering amplitudes; one-loop Feynman diagrams
• Language: croatian
• URN:NBN: urn:nbn:hr:217:388058
• Study programme: Title: Physics; Study programme type: university; Study level: postgraduate; Academic / professional title: doktor/doktorica znanosti, područje prirodnih znanosti, polje fizika (doktor/doktorica znanosti, područje prirodnih znanosti, polje fizika)
• Type of resource: Text
• Extent: 53 str.
• File origin: Born digital
• Access conditions: Open access
• Created on: 2017-08-21 10:02:25