Problem vremena u kanonskoj kvantnoj gravitaciji

master's thesis

• Title (english): The problem of time in canonical quantum gravity
• Author: Sven Hrastić
• Mentor: Hrvoje Nikolić (mentor)
• Mentor: Ivica Smolić (komentor)
• Committee member: Ivica Smolić (član povjerenstva)
• Committee member: Hrvoje Nikolić (član povjerenstva)
• Committee member: Maro Cvitan (član povjerenstva)
• Committee member: Krešimir Kumerički (član povjerenstva)
• Committee member: Matko Milin (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); (Theoretical Physics Division of Particles and Fields); Zagreb
• Defense date and country: 2025-02-26, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics; Physics of Elementary Particles and Fields

Abstract

U ovom diplomskom radu će se u detalje istražiti kanonska formulacija opće relativnosti i pokušat će se odgovoriti na pitanje što je to problem vremena u kvantnoj gravitaciji. Kroz razradu formalizma kanonske opće relativnosti vidjet će se da postoje jednadžbe evolucije, no ne onakve kakve zadovoljavaju potrebe kvantne teorije. Pogledat će se pristup rješavanju problema vremena koji je objašnjen u [K.V. Kuchař, Time and interpretations of quantum gravity, Int. J. Mod.Phys. D 20, Suppl. 1 (2011)... More 3-86.]. U drugom poglavlju će se otprilike pokušati objasniti što je to problem vremena. Kasnije kada razradimo formalizam (3+1) opće relativnosti krenut će se na detaljnu analizu ograničenja superhamiltonijana i superimpulsa te kako bi se mogli svesti u kvantnu formu. Pri tome će doći do mnogih problema koji će se probati ilustrativno riješiti na nekim sustavima jednostavnijim od pune geometrodinamike. Proći će se kroz sustave koji se mogu svesti na tzv. višeprstnu Schrödingerovu jednadžbu. Less

Abstract (english)

In this thesis we will in detail explore canonical formulation of general relativity and we will try to answer the question what is the problem of time in quantum gravity. While working out the formalism of general relativity we will see that there exist equations of evolution, but not the ones suitable for the needs of quantum theory. We will take a look at the approach that's explained in [K.V. Kuchař, Time and interpretations of quantum gravity, Int. J. Mod.Phys. D 20, Suppl. 1 (2011)... More 3-86.]. In second paragraph problem of time will be explained on a simple system. Later when the formalism of (3+1) general relativity is worked out we will in detail explore super-Hamiltonian and super momentum constraints and how to quantize them. In these attempts at quantization there will be many problems that will be solved on simpler systems than full geometrodynamics. We will go through systems that can be cast into so called many fingered Schrödinger equation. Less

• Keywords: opća relativnost; foliacija; tenzor; Schrödingerova jednadžba; Diracova kvantizacija
• Keywords (english): general relativity; foliation; tensor; Schrödinger equation; Dirac quantization
• Language: croatian
• URN:NBN: urn:nbn:hr:217:817138
• 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: 2025-02-23 20:10:23