Title Time and causal ordering in quantum mechanics and quantum field theory Title (croatian) Vremensko i kauzalno uređenje u kvantnoj mehanici i kvantnoj teoriji polja Author Vanessa Brzić Mentor Časlav Brukner (mentor) Mentor Krešimir Kumerički (komentor)Committee member Krešimir Kumerički (predsjednik povjerenstva)Committee member Ivica Smolić (član povjerenstva)Committee member Matko Milin (član povjerenstva)Committee member Davor Horvatić (član povjerenstva)Committee member Ivica Friščić (član povjerenstva)Granter University of Zagreb Defense date and country 2022-09-30, Croatia Scientific / art field, NATURAL SCIENCES Abstract One of the grates difficulties arising within the attempts to reconcile the quantum theory and general relativity stems from the profound differences in the ways the notions of space, time, reference frame, and causation enter the two formulations. It is often argued that both theories should compromise on their respective understandings for this merging (in the theory of quantum gravity) to be possible. Motivated by this thought, in the thesis we will focus on the assumptions brought up within the newly established framework of quantum causality and the formulation of time within the conditional probabilistic approach (so-called Page-Wotters formalism). With these extensions, there are already strong conceptual differences at the level of comparison between quantum mechanics and quantum field theory, the resolution of which would represent a preliminary step towards the ideas of quantum gravity. Stirred by this friction, the goal of the dissertation was to re-examine the notions of temporal and causal ordering in the context of modern approaches to quantum theory in relation to approaches within perturbative field theory. As an interesting playground for challenging our understanding we took time ordering operator and investigated it in several different, albeit related contexts: (1) as it appears in the Schrödinger solution of standard quantum mechanics with time dependent Hamiltonian, (2) in Page-Wotters formalism, considering a constraint equation with several quantum clocks and (3) in the context of quantum field theory and Feynman propagator. The research objective was to understand whether one can view the action of the time ordering operator as enabling a superposition of different time-ordered configurations, introducing time indefiniteness in the aforementioned settings. Regarding quantum fields, we questioned the possibility of the operational interpretation of the (scattering theory) virtual particle exchange process, often understood in terms of two time-ordered processes happening via particle/antiparticle exchange. Our approach was to look at the time-ordered exponentials up to the second order and attempt to isolate one of the ordering ’branches,’ projecting a superposition to a definite state. We found that one cannot break the time ordering superposition of the exponential expansion in the context of standard quantum mechanics coupling it with the ancilla potential; however, one can perform this kind of projection in the context of timeless quantum mechanics with two or more quantum clocks. We then approached these considerations in the context of quantum fields, using the Schrödinger functional representation, seeking to implement the Page-Wotters approach and the previously developed toy model.
Abstract (croatian) Jedna od glavnih poteškoća koja se javlja u pokušajima pomirenja kvantne teorije i opće teorije relativnosti proizlazi iz dubokih razlika u načinima na koje su pojmovi prostora, vremena, referentnog sustava i kauzalnosti implementirani u navedene teorije. često se tvrdi da bi obje teorije trebale istrpiti kompromis u konceptualnim razumijevanjima spomenutog, kako bi njihovo spajanje (u teoriju kvantne gravitacije) bilo moguće. Potaknuti tom mišlju, u ovom ćemo se radu usredotočiti na pretpostavke iznesene unutar novouspostavljenog okvira kvantne kauzalnosti i formulacije vremena preko uvjetnog probabilističkog pristupa (tzv. Page-Wottersov formalizam ). Ovim proširenjima konceptualne razlike već na razini usporedbe kvantne mehanike s obzirom na kvantnu teoriju polja postaju snažne, a njihovo razumijevanje predstavlja preliminarni korak prema idejama kvantne gravitacije. Potaknuti time, cilj ove disertacije bio je preispitati pojmove vremenskog i kauzalnog uređenja u kontekstu modernih pristupa kvantnoj teoriji u odnosu na pristupe unutar perturbativne teoriji polja. Kao zanimljivu okosnica za ispitivanje našeg razumijevanja uzeli smo operator vremenskog uređenja i istražili ga u nekoliko različitih, iako povezanih konteksta: (1) kako se pojavljuje u Schrödingerovom rješenju standardne kvantne mehanike s vremenski ovisnim Hamiltonijanom, (2) u Page-Wottersovom formalizam, gdje smo razmatrali jednadžbe ograničenja s nekoliko kvantnih satova i (3) u kontekstu kvantne teorije polja i Feynmanovog propagatora. Cilj istraživanja bio je razumjeti može li se promatrati djelovanje operatora vremenskog uređenja kao omogućavanje superpozicije različitih vremenski uređenih konfiguracija, uvodeći vremensku neodređenost u gore navedene postavke. Što se tiče kvantnih polja, doveli smo u pitanje mogućnost operativnog tumačenja procesa virtualne izmjene čestica (teorija raspršenja), koji se često shvaća u terminima dva vremenski uređena procesa koji se odvijaju putem izmjene čestica/antičestica. Naš je pristup bio promatrati vremenski uređene eksponencijale do drugog reda i pokušati izolirati jednu od ’grana’ reda, projicirajući superpoziciju na određeno stanje. Otkrili smo da se superpozicija vremenskog uređenja eksponencijalne ekspanzije ne može proicirati na definitno stanje jedne od ’grana’ superpoziciju, u kontekstu standardne kvantne mehanike, spajanjem s potencijalom pomoćnog sustava; međutim, ova vrsta projekcije može se izvesti u kontekstu Page-Wotters formalisma s dva ili više kvantnih satova. Zatim smo pristupili ovim razmatranjima u kontekstu kvantne teorije polja, koristeći Schrödingerovu funkcionalnu reprezentaciju, nastojeći implementirati Page-Wotters pristup i prethodno razvijeni ’toy model’.
Keywords
superposition of temporal orders
quantum causality
perturbative quantum field theory
Feynman propagator
Page-Wotters formalism
Schrödinger functional representation
Keywords (croatian)
superpozicija vremenskih uređenja
kvantna kauzalnost
perturbativna kvantna teorija polja
Feynmanov propagator
Page-Wottersov formalizam (bezvremenski formalizam)
Schrödingerova funkcionalna reprezentacija
Language english URN:NBN urn:nbn:hr:217:244872 Study programme Title: Physics; specializations in: Research Type of resource Text File origin Born digital Access conditions Open access Terms of use Created on 2022-10-25 10:10:12
