The geometry of the Standard Model

master's thesis

• Title (croatian): Geometrija Standardnog Modela
• Author: Filip Požar
• Mentor: Tajron Jurić (mentor)
• Mentor: Ivica Smolić (komentor)
• Committee member: Ivica Smolić (predsjednik povjerenstva)
• Committee member: Tajron Jurić (član povjerenstva)
• Committee member: Nikola Poljak (član povjerenstva)
• Committee member: Maro Cvitan (član povjerenstva)
• Committee member: Petar Žugec (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); Zagreb
• Defense date and country: 2022-10-10, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract

This Master’s Thesis is an almost completely self-contained outline of the Standard Model (SM) in the framework of gauge theory. The tools from differential geometry, differential topology and spin structure necessary for mathematical description of gauge theories were built and their examples in General theory of relativity (GR) were shown. Special attention was paid to principal and associated bundles which are central mathematical objects used to define gauge theories. Then the SM was shortly outlined in the style of undergraduate courses Elementary particle physics, focusing mostly on its symmetries and the structure of its Lagrangian. In the end, the developed mathematical structures were applied on the concrete gauge theory of the Standard Model by rigorously defining every term of its Lagrangian in a geometrical way.

Abstract (croatian)

Ovaj diplomski rad je gotovo samodostatno rigorozno izlaganje Standardmog modela (SM) kao baždarne teorije. Izgradili smo pojmove iz diferencijalne geometrije, diferencijalne topologije i spinske strukture nužne za matematički opis baždarnih teorija i usput ih demonstrirali primjerima na Općoj teoriji relativnosti (OTR). Posebna pozornost je dana glavnim i pridruženih svežnjevima koji su centralni matematički objekti za definiranje baždarnih teorija. Zatim je ukratko izložen SM u stilu diplomskih kolegija Fizika elementarnih čestica, fokusirajući se najviše na njegove simetrije i strukturu njegovog lagranžijana. Na kraju, primijenjene su razvijene matematičke strukture na konkretnu baždarnu teoriju Standardnog modela rigoroznim definiranjem svakog člana njegovog lagranžijana na geometrijski način.

• Keywords: Standard Model; differential geometry; topology; symmetries; principal bundle; associated bundle; spinor
• Keywords (croatian): standardni model; diferencijalna geometrija; topologija; simetrije; glavni svežanj; pridruženi svežanj; spinor
• Language: english
• URN:NBN: urn:nbn:hr:217:063501
• 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: 2022-12-05 14:16:50