Hopfove algebre u fizici

master's thesis

• Title (english): Hopf algebras in physics
• Author: Nikola Herceg
• Mentor: Tajron Jurić (mentor)
• Mentor: Ivica Smolić (komentor)
• Committee member: Ivica Smolić (predsjednik povjerenstva)
• Committee member: Tajron Jurić (član povjerenstva)
• Committee member: Matko Milin (član povjerenstva)
• Committee member: Nikola Poljak (član povjerenstva)
• Committee member: Maro Cvitan (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); Zagreb
• Defense date and country: 2021-11-19, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract

Uvodimo Hopfove algebre i primjenjujemo ih u teoriji polja na nekomutativnom prostoru, višečestičnom anyonskom sustavu, renormalizaciji Feynmanovih dijagrama te pokazujemo bicrossproduct strukturu κ-Poincareove algebre. Ilustriramo neke fenomene koji se pojavljuju u teoriji polja na nekomutativnom prostoru poput UV/IR miješanja i neplanarnih dijagrama, dajemo vezu između kvazitriangularne strukture i cistične statistike te izvodimo Yang- Baxterovu jednadžbu. Feynmanove dijagrame opisujemo pomoću Hopfove algebre ukorijenjenih stabala slijedeći pristup Connesa i Kreimera. Na kraju faktoriziramo κ-Poincare algebru analogno semidirektnom produktu Poincareove algebre.

Abstract (english)

We introduce Hopf algebras and apply them to non-commutative field theory, multiparticle anyonic system, renormalization of Feynman diagrams and bicrossproduct structure of the κ-Poincare Hopf algebra. Several phenomena arising from the spacetime non-commutativity are illustrated, such as UV/IR mixing and non-planar diagrams. The connection between the quasitriangular structure and particle statistics is demonstrated via derivation of the Yang-Baxter equation. Feynman diagrams are renormalized using the Connes-Kreimer technique of rooted trees. In the end we show how κ-Poincare algebra factorises in the way analogous to the semidirect structure of the Poincare group.

• Keywords: Hopf; algebra; koalgebra; bialgebra; kvazitriangularna; statistika; nekomutativnost; renormalizacija; BPHZ; kvantna grupa
• Keywords (english): Hopf; alebra; coalgebra; bialgebra; quasitriangular; statistics; non-commutativity; renormalization; BPHZ; bicrossproduct; quantum group
• Language: croatian
• URN:NBN: urn:nbn:hr:217:879182
• 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: 2021-12-09 16:50:57