Algebre L_∞ u teoriji polja

master's thesis

• Title (english): L _∞ algebras in field theory
• Author: Jelena Anić
• Mentor: Larisa Jonke (mentor)
• Mentor: Amon Ilakovac (mentor)
• Committee member: Amon Ilakovac (predsjednik povjerenstva)
• Committee member: Larisa Jonke (član povjerenstva)
• Committee member: Nikola Poljak (član povjerenstva)
• Committee member: Matko Milin (član povjerenstva)
• Committee member: Ivica Smolić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; Zagreb
• Defense date and country: 2019-12-20, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract

Algebra L_∞ je poopćenje pojma Liejeve algebre. Najprije uvodimo L_∞ formalizam, koji zatim primjenjujemo na standardnu baždarnu Yang-Millsovu i Chern- Simonsovu teoriju. Upotrebom viših zagrada potvrđujemo da su svi poopćeni Jacobijevi identiteti zadovoljeni. Algebra L_∞ daje sistematičnu metodu za nalaženje deformacija neke postojeće teorije, što pokazujemo na primjeru Chern-Simonsove teorije koju vežemo sa BF teorijom, odnosno uvodimo skalarnu 0-formu i 2-formu. Nakon konstrukcije najopćenitijih jednadžbi gibanja i baždarnih transformacija sastavljenih od skalara, 1-forme i 2-forme, algebru tenzorskog produkta i L_∞ identitete koristimo kako bismo našli relacije koje povezuju strukturne funkcije. Rezultat teorije konstuirane na taj način je poznat pod nazivom Courantov sigma model.

Abstract (english)

L∞ algebra is a generalisation of the notion of a Lie algebra. We shall first introduce L∞ formalism and then apply it on standard Yang-Mills and Chern-Simons gauge theories. Using the higher brackets, we show that all strong homotopy Jacobi identities are satisfied. Furthermore, L∞ algebra provides a systematic way of searching for deformations of some existing theories, which we shall demonstrate on the Chern- Simons theory by coupling it to a BF theory, i.e., scalar 0-form and 2-form. Having constructed the most general equations of motion and gauge transformations composed of a scalar, 1-form and 2-form fields, we use the tensor product algebra and L∞ identities to find restrictions on structure functions. The theory we obtain in this way is known as Courant sigma model.

• Keywords: algebra L_∞; poopćeni Jacobijevi identiteti; Yang-Millsova teorija; Chern-Simonsova teorija
• Keywords (english): L_∞ algebra; strong homotopy identities; Yang-Mills theory; Chern-Simonstheory
• Language: croatian
• URN:NBN: urn:nbn:hr:217:660745
• 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: 2020-03-10 15:32:18