Kozmološki singulariteti u formalizmu integrala po putovima

master's thesis

• Title (english): Cosmological singularities in path integral approach
• Author: Mario Tanfara
• Mentor: Ivica Smolić (mentor)
• Committee member: Ivica Smolić (predsjednik povjerenstva)
• Committee member: Maro Cvitan (član povjerenstva)
• Committee member: Nikola Poljak (član povjerenstva)
• Committee member: Davor Horvatić (član povjerenstva)
• Committee member: Matko Milin (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); Zagreb
• Defense date and country: 2022-02-25, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract

Uvodimo formalizam integrala po putevima na primjeru nerelativističkog sustava s jednim fizikalnim stupnjem slobode. Za model zatvorenog svemira s FRLW metrikom i pozitivnom kozmološkom konstantom, gdje je jedan stupanj slobode faktor skale, analogijom definiramo mjeru funkcionalnog integrala. Raspravljamo o hamiltonijanskim sustavima s ograničenjima, medu kojima je i opća teorija relativnosti, te Fradkin–Vilkoviskyjevim teoremom dobivamo baždarno invarijantan, unitarni, uvjetno konvergentni funkcionalni integral. Po uzoru na Turoka i suradnike Picard–Lefschetzovim formalizmom identificiramo jedinstvenu relevantnu sedlenu točku akcije i jedinstvenu konturu po kojoj je apsolutna konvergencija osigurana. Postavljajući ”no-boundary” rubne uvjete, dobivamo potiskujući poluklasični faktor.

Abstract (english)

By considering a nonrelativistic system with one physical degree of freedom we introduce the path integral formalism. For a closed Universe with FLRW metric and a positive cosmological constant, where the degree of freedom is the scale factor, by analogy we define the measure of the functional integral. We discuss Hamiltonian systems with constraints, among them general relativity, and by utilizing the Fradkin– Vilkovisky theorem obtain a gauge invariant, unitary, conditionally convergent functional integral. Following the works of Turok et al. we use the Picard–Lefschetz formalism to identify a unique relevant saddle point of the action and a unique contour along which absolute convergence is certain. Imposing the ”no-boundary” initial conditions, we get a semiclassical suppression factor.

• Keywords: minisuperprostor; Integrali po putevima; Hamiltonijanski sustavi s ograničenjima; Fradkin–Vilkoviskyjev teorem; Picard–Lefschetzova integracija; ”Noboundary” prijedlog
• Keywords (english): minisuperspace; path integrals; Hamiltonian systems with constraints; Fradkin–Vilkovisky theorem; Picard–Lefschetz integration; no-boundary proposal
• Language: croatian
• URN:NBN: urn:nbn:hr:217:831413
• 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: 2022-03-21 10:38:57