Fizika u infracrvenom području energija

master's thesis

• Title (english): Physics in the infrared energy region
• Author: David Orešković
• Mentor: Larisa Jonke (mentor)
• Mentor: Maro Cvitan (komentor)
• Committee member: Maro Cvitan (predsjednik povjerenstva)
• Committee member: Larisa Jonke (član povjerenstva)
• Committee member: Matko Milin (član povjerenstva)
• Committee member: Ivica Smolić (član povjerenstva)
• Committee member: Nikola Poljak (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); Zagreb
• Defense date and country: 2021-07-14, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract

U ovom radu su analizirane trokutne relacije koje povezuju dinamiku fizikalnih teorija u infracrvenom (IR) spektru energija. Vrhovi IR trokuta se odnose na mekane teoreme, asimptotske simetrije i memorijske efekte te veza između njih ”odjekuje” kroz mnogo područja fizike s bezmasenim česticama. Ovdje je istražena struktura dvaju vrhova IR trokuta u gravitaciji; konkretnije, pokazano je da su asimptotske simetrije i mekani teoremi povezani Wardovim identitetom. Prvo je napravljena konstrukcija Carter-Penroseovih dijagrama prostor-vremena Minkowskog budući da su isti pogodni za analizu trajektorija bezmasenih čestica u asimptotski ravnim prostorima. Data je rigorozna definicija buduće i prošle svjetlosne beskonačnosti kao trodimenzionalnih površina na kojima bezmasene čestice završavaju i započinju svoje putanje te su iste parametrizirane s prikladnim setom koordinata. U četvrtom poglavlju je prvo analizirana Bondi-Sachsova metrika, nakon čega su raspisane Einsteinove jednadžbe iskazane preko koeficijenata spomenute metrike. Nametnuti su rubni uvjeti koji čuvaju asimptotsku ravnost i pronađena rješenja Einsteinovih jednadžbi u prostornoj beskonačnosti. Koristeći ova rješenja, istražena je forma asimptotskih generatora difeomorfizama te je na temelju istih uočeno postojanje beskonačno očuvanih naboja asociranih s translacijama u prostor-vremenu. Analiza asimptotskih simetrija je završena s izvodom supertranslacijskog Wardovog identiteta koji povezuje S-matrične elemente sa i bez umetanja niskoenergetskog gravitona. U petom poglavlju je uveden formalizam kojim je opisana gravitacija kao efektivna teorija polja. Dan je kratki uvod u gravitacijske valove i provedena fizikalna interpretacija određenih veličina definiranih u četvrtom poglavlju. Ovdje je ukratko opisan i treći vrh infracrvenog trokuta, odnosno gravitacijski memorijski efekt. Poglavlje je zaključeno s kvantizacijom gravitacije kao efektivne teorije polja. Konačno, preko Feynmanovih dijagrama je izveden Weinbergov teorem mekanog gravitona te je pokazano da iz istog slijedi supertranslacijski Wardov identitet.

Abstract (english)

This thesis deals with the analysis of triangular relations which connect the dynamics of physical theories in infrared (IR) spectrum of energies. Corners of the IR triangle represent soft theorems, asymptotic symmetries and memory effects. In recent years, it was shown that connections between these ”echo” throughout many physical theories with massless particles. Here, research of two corners of the IR triangle is conducted for the case gravity; more precisely, it is shown that asymptotic symmetries and soft theorems are connected via Ward identity. Firstly, Carter-Penrose diagrams are constructed for Minkowski spacetime since these are fit for description of lightlike trajectories in asymptotically flat spaces. Future and past null infinity as three-dimensional surfaces at which massles particles end and begin their trajectories are rigorously defined and parametrised by appropriate coordinates. In fourth chapter, Bondi-Sachs metric is analysed and Einstein equations written in terms of metric coefficients. Boundary conditions which preserve asymptotic flatness are imposed and solutions to Einstein equations are found in spatial infinity. Using these solutions, structure of asymptotic generators of diffeomorphisms is analysed and it is observed that these imply the existence of infinite number of consereved charges associated with spacetime translations. The analysis of asymptotic symmetries is concluded with derivation of supertranslational Ward identity which connects the S-matrix elements with and without the insertion of soft graviton. In fifth chapter, formalisam of gravity as an effective field theory is introduced. Gravitational waves are briefly revised and certain variables defined in chapter four are physically interpreted. Here, third corner of the infrared triangle, that is, the gravitational memory effect, is also briefly touched upon. Chapter is concluded with quantisation of gravity as effective field theory. Finally, Weinberg’s soft graviton theorem is derived by using Feynman diagrams and it is shown that supertranslationalWard identity follows from this theorem.

• Keywords: gravitacija; graviton; simetrije; infracrveno; supertranslacije
• Keywords (english): gravity; graviton; symmetries; infrared; supertranslations
• Language: croatian
• URN:NBN: urn:nbn:hr:217:974510
• 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: 2021-07-23 10:49:32