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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. 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. |
